Finite Group Databasebeta

← #15870770

Subgroups — #15870770

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124622C211yesmaximal, characteristic
2#13123775C211yesmaximal, characteristic, complemented
3#13123263C211yesmaximal, characteristic
4#13115778C211yesmaximal, characteristic, complemented
5#13115610C211yesmaximal, characteristic, complemented
6#13115435C211yesmaximal, characteristic, complemented
7#13115114C211yesmaximal, characteristic
8#13115110C211yesmaximal, characteristic
9#13114855C211yesmaximal, characteristic
10#13114719C211yesmaximal, characteristic, complemented
11#13114717C211yesmaximal, characteristic, complemented
12#13114709C211yesmaximal, characteristic, complemented
13#13114677C211yesmaximal, characteristic
14#13114672C211yesmaximal, characteristic
15C13×#1922C211yesmaximal, characteristic, complemented
16C2×#88161C2211yescharacteristic
17C2×#88155C2211yescharacteristic
18#11719227C2211yescharacteristic
19#11719222C2211yescharacteristic
20C13×#427C2211yescharacteristic
21C13×#424C2211yescharacteristic
22C13×#405C2211yescharacteristic
23C2×#88065C2211yescharacteristic
24C2×#88062C2211yescharacteristic
25#11718783C2211yescharacteristic
26#11718779C2211yescharacteristic
27M16×Dic13C2211yescharacteristic
28#11718774C2211yescharacteristic
29C2×#88059C2211yescharacteristic
30#11718763C2211yescharacteristic
31C2×#88055C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34#11718663C2211yescharacteristic
35#11718659C2211yescharacteristic
36#11718658C2211yescharacteristic
37#11718658C2211yescharacteristic
38C4×#6101C2211yescharacteristic
39C2×#88045C2211yescharacteristic
40C2×#88043C2211yescharacteristic
41#11718552C411yescharacteristic, complemented
42#11718551C411yescharacteristic, complemented
43#11718538C411yescharacteristic, complemented
44#11718536C411yescharacteristic, complemented
45#11718532C411yescharacteristic, complemented
46#11718531C411yescharacteristic, complemented
47#11718518C411yescharacteristic, complemented
48#11718515C411yescharacteristic, complemented
49#11718492—21no—
50#11718492—21no—
51#11718489—21no—
52#11718489—21no—
53#11718369—21no—
54D13×#97—21no—
55#11718350—21no—
56C4×#6094—21no—
57C13×#341C2211yescharacteristic
58C13×#339C2211yescharacteristic
59C13×#339C2211yescharacteristic
60C13×#336C2211yescharacteristic
61#11718150C2211yescharacteristic
62#11718147C2211yescharacteristic
63#11718142C2211yescharacteristic
64#11718124C2211yescharacteristic
65#11718124C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×#6127C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C13×#117C2311yescharacteristic
73C13×#117C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75#88180C2311yescharacteristic
76C2×#6101—21no—
77C2×C4×Dic13C2311yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C2×#6099C2311yescharacteristic
80C2×#6099C2311yescharacteristic
81C22×#1055C2311yescharacteristic
82C22×#1055C2311yescharacteristic
83#88161—22no—
84#88161Q814yescomplemented
85#88155—22no—
86#88155—22no—
87C2×#6094—21no—
88C2×#6094—21no—
89C2×C8×D13—21no—
90C2×C8×D13—21no—
91#88147C2×C411yescharacteristic
92#88147C2×C411yescharacteristic
93#88144C2×C411yescharacteristic
94#88144C2×C411yescharacteristic
95#88142C2×C411yescharacteristic
96#88142C2×C411yescharacteristic
97#88141C2×C411yescharacteristic
98#88141C2×C411yescharacteristic
99#88135—21no—
100#88135—21no—
101#88132—21no—
102#88132—21no—
103#88126—21no—
104C42×D13—21no—
105C4×Dic26—21no—
106C4×Dic26—21no—
107C13×#107C2×C411yescharacteristic
108C13×#107C2×C411yescharacteristic
109C13×#106C2×C411yescharacteristic
110C13×#106C2×C411yescharacteristic
111C13×C4⋊C8—21no—
112C13×C4⋊C8—21no—
113C13×#97—21no—
114C4×C8×C13—21no—
115#88071—21no—
116#88065—22no—
117#88062—22no—
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88059—22no—
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88055—21no—
125#88055D411yescharacteristic
126#88055D411yescharacteristic
127#88055D411yescharacteristic
128#88055D411yescharacteristic
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054C2×C411yescharacteristic
134#88054C2×C411yescharacteristic
135#88054C2×C411yescharacteristic
136#88054C2×C411yescharacteristic
137C8×Dic13—21no—
138C8×Dic13—21no—
139C8×Dic13—22no—
140#88050C2×C411yescharacteristic
141#88050C2×C411yescharacteristic
142#88049C2×C411yescharacteristic
143#88049C2×C411yescharacteristic
144#88048C2×C411yescharacteristic
145#88048C2×C411yescharacteristic
146#88047C2×C411yescharacteristic
147#88047C2×C411yescharacteristic
148#88045—22no—
149#88043—21no—
150#88043—21no—
151#88043—22no—
152C4×#1055—21no—
153C4×#1055—21no—
154#21629—131nomaximal, Sylow
155C22×C4×C13—21no—
156C22×C4×C13C2411yescharacteristic
157C2×C22⋊D13—21no—
158C22×Dic13—21no—
159C22×Dic13#4111yescharacteristic
160C22×Dic13#4111yescharacteristic
161#6127—21no—
162#6127—21no—
163#6127C2×Q812yes—
164#6127#4112yes—
165C2×D52C22×C411yescharacteristic
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26C22×C411yescharacteristic
172C13×M16—21no—
173C13×M16—21no—
174C13×M16—21no—
175C13×M16C2×Q812yes—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13—21no—
182C2×C8×C13C22×C411yescharacteristic
183C2×C8×C13C22×C411yescharacteristic
184C2×C8×C13C2×D411yescharacteristic
185C2×C8×C13C2×D411yescharacteristic
186C13×C4⋊C4C22×C411yescharacteristic
187C13×C4⋊C4C22×C411yescharacteristic
188C13×C4⋊C4C22×C411yescharacteristic
189C13×C4⋊C4C22×C411yescharacteristic
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C22⋊Dic13—21no—
197#6103—21no—
198#6103—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13C22×C411yescharacteristic
202C4⋊Dic13C22×C411yescharacteristic
203#6101—21no—
204#6101—21no—
205#6101—21no—
206#6101—21no—
207#6101—21no—
208#6101—21no—
209#6101—42no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—21no—
215C4×Dic13C22×C411yescharacteristic
216C4×Dic13C22×C411yescharacteristic
217C4×Dic13C2×D411yescharacteristic
218C4×Dic13C2×D411yescharacteristic
219#6099—21no—
220#6099—21no—
221#6099—21no—
222#6099#4112yes—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055C22×C411yescharacteristic
228C2×#1055C22×C411yescharacteristic
229C2×#1055C2×D411yescharacteristic
230C2×#1055C2×D411yescharacteristic
231C2×#1055C2×Q812yes—
232C2×#1055#4112yes—
233#6094—24no—
234#6094—24no—
235C8×D13—24no—
236C8×D13—24no—
237#3076—131no—
238#2961—131no—
239#2875—131no—
240#1986—131no—
241#1950—131no—
242#1922—131no—
243#1922D1311yescharacteristic, complemented
244#1866—131no—
245#1866—131no—
246#1806—131no—
247#1773—131no—
248#1772—131no—
249#1771—131no—
250#1765—131no—
251#1764—131no—
252C23×C13C2×#4111yescharacteristic
253C22×D13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13C23×C411yescharacteristic
262C2×C4×C13C22×D411yescharacteristic
263C2×C4×C13C22×Q811yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C22⋊D13—22no—
268C22⋊D13—22no—
269C2×Dic13—21no—
270C2×Dic13—22no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13C4×D411yescharacteristic
278C2×Dic13C4×D411yescharacteristic
279C2×Dic13C4×D411yescharacteristic
280C2×Dic13C4×D411yescharacteristic
281D52—21no—
282D52C4×Q812yes—
283C4×D13—22no—
284C4×D13—22no—
285C4×D13—81no—
286C4×D13—81no—
287Dic26—21no—
288Dic26—81no—
289Dic26—81no—
290Dic26C4×Q812yes—
291C8×C13—21no—
292C8×C13—21no—
293C8×C13—22no—
294C8×C13—21no—
295C8×C13—21no—
296C8×C13—41no—
297#1055—21no—
298#1055—21no—
299#1055—22no—
300#1055—41no—
301#1055C22⋊Q812yes—
302#1055C22⋊Q812yes—
303C2×#131—131no—
304C2×#131—131no—
305#533—131no—
306C4×#41—131no—
307#479—131no—
308#479—131no—
309#478—131no—
310#478—131no—
311#477—131no—
312#476—131no—
313#475—131no—
314#474—131no—
315#446—261no—
316#446—261no—
317#446—261no—
318#446—261no—
319C2×#108—131no—
320C2×#108—131no—
321#427—131no—
322#427C2×D1311yescharacteristic
323#424—131no—
324#424C2×D1311yescharacteristic
325#423—131no—
326C2×C4⋊C8—131no—
327C2×#104—131no—
328C2×#104—131no—
329#416—131no—
330#416—131no—
331#405—131no—
332#405—131no—
333#405—131no—
334#405—261no—
335#405—261no—
336#405C2×D1311yescharacteristic
337C4×M16—131no—
338C4×M16—261no—
339C2×#97—131no—
340C2×#97—131no—
341C2×#97—261no—
342C2×C4×C8—131no—
343C4×C4⋊C4—131no—
344#341—131no—
345#341C2×D1311yescharacteristic
346#339—131no—
347#339—131no—
348#339—131no—
349#339—131no—
350#339C2×D1311yescharacteristic
351#339C2×D1311yescharacteristic
352#336—131no—
353#336C2×D1311yescharacteristic
354C22×C13—21no—
355C22×C13—21no—
356C22×C13C2×C4×D411yescharacteristic
357C22×C13#52911yescharacteristic
358C22×C13#53311yescharacteristic
359C2×D13—22no—
360C2×D13—41no—
361C2×D13—41no—
362C4×C13—41no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—41no—
366C4×C13—81no—
367C4×C13C2×C4×Q811yescharacteristic
368C4×C13C4×#4111yescharacteristic
369C4×C13C2×C22⋊Q811yescharacteristic
370C4×C13#52511yescharacteristic
371Dic13—21no—
372Dic13—21no—
373Dic13—21no—
374Dic13—21no—
375Dic13—22no—
376Dic13—42no—
377Dic13—41no—
378Dic13—41no—
379C2×#41—131no—
380#131—134no—
381#131—262no—
382#131—262no—
383#131—262no—
384C2×M16—131no—
385C2×M16—131no—
386C2×M16—261no—
387C2×M16—261no—
388C2×M16C22×D1311yescharacteristic
389C2×M16C22×D1311yescharacteristic
390C22×C8—131no—
391C22×C8—131no—
392C22×C8—261no—
393C22×C8—261no—
394C22×C8C22×D1311yescharacteristic
395C22×C8C22×D1311yescharacteristic
396C4⋊Q8—131no—
397C4⋊Q8—131no—
398#125—131no—
399#125—131no—
400C22⋊Q8—261no—
401C22⋊Q8—261no—
402C4×Q8—131no—
403C4×Q8—131no—
404C4×Q8—261no—
405C4×Q8—261no—
406C4×D4—131no—
407C4×D4—131no—
408C4×D4—261no—
409C4×D4—261no—
410#117—131no—
411#117—261no—
412#117C22×D1311yescharacteristic
413#117C22×D1311yescharacteristic
414C2×C4⋊C4—261no—
415C2×C42—131no—
416C2×C42—131no—
417C2×C42—261no—
418C2×C42C22×D1311yescharacteristic
419#108—262no—
420#108—262no—
421#107—131no—
422#107—131no—
423#107C4×D1311yescharacteristic
424#107C4×D1311yescharacteristic
425#106—131no—
426#106—131no—
427#106C4×D1311yescharacteristic
428#106C4×D1311yescharacteristic
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—131no—
432C4⋊C8—131no—
433C4⋊C8—131no—
434C4⋊C8—131no—
435C4⋊C8—261no—
436C4⋊C8—261no—
437C4⋊C8—261no—
438C4⋊C8—261no—
439#104—262no—
440#104—262no—
441#103—131no—
442#103—131no—
443#103—131no—
444#103—131no—
445#102—131no—
446#102—131no—
447#102—131no—
448#102—131no—
449#97—21no—
450#97—131no—
451#97—131no—
452#97—131no—
453#97—131no—
454#97—262no—
455#97—261no—
456#97—261no—
457#97—261no—
458#97—261no—
459C4×C8—21no—
460C4×C8—261no—
461C4×C8—261no—
462C4×C8—261no—
463C4×C8—262no—
464C4×C8—261no—
465#95—261no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13C4×C22⋊Q811yescharacteristic
469C2×C13#295611yescharacteristic
470C2×C13#295711yescharacteristic
471D13—42no—
472#41—132no—
473#41—132no—
474#41—261no—
475#41—261no—
476C2×Q8—131no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×D4—131no—
480C2×D4—261no—
481C22×C4—21no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4C23×D1311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—132no—
493M16—264no—
494M16—264no—
495M16—261no—
496M16—261no—
497M16—261no—
498M16Q8×D1312yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—131no—
506C2×C8—131no—
507C2×C8—132no—
508C2×C8—132no—
509C2×C8—131no—
510C2×C8—131no—
511C2×C8—264no—
512C2×C8—264no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8C2×C4×D1311yescharacteristic
518C2×C8C2×C4×D1311yescharacteristic
519C2×C8D4×D1311yescharacteristic
520C2×C8D4×D1311yescharacteristic
521C4⋊C4—131no—
522C4⋊C4—131no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—522no—
532C4⋊C4C2×C4×D1311yescharacteristic
533C4⋊C4C2×C4×D1311yescharacteristic
534C4⋊C4C2×C4×D1311yescharacteristic
535C4⋊C4C2×C4×D1311yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—261no—
539C22⋊C4—261no—
540C22⋊C4—261no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—131no—
546C42—131no—
547C42—131no—
548C42—131no—
549C42—261no—
550C42—261no—
551C42—261no—
552C42—261no—
553C42—261no—
554C13#2162911yescharacteristic, complemented, Sylow
555C23—261no—
556C23#41×D1311yescharacteristic
557Q8—132no—
558Q8—261no—
559Q8—1041no—
560Q8—1041no—
561D4—132no—
562D4—262no—
563D4—262no—
564D4—261no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—131no—
573C2×C4—131no—
574C2×C4—131no—
575C2×C4—131no—
576C2×C4—261no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—1041no—
587C2×C4—1041no—
588C2×C4C22×C4×D1311yescharacteristic
589C2×C4C2×D4×D1311yescharacteristic
590C2×C4C2×Q8×D1311yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C8—21no—
595C8—21no—
596C8—22no—
597C8—21no—
598C8—21no—
599C8—41no—
600C8—132no—
601C8—132no—
602C8—261no—
603C8—261no—
604C8—262no—
605C8—521no—
606C22—21no—
607C22—21no—
608C22—262no—
609C22—521no—
610C22—521no—
611C22C4×D4×D1311yescharacteristic
612C22#1171939311yescharacteristic
613C22#1171941111yescharacteristic
614C4—41no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—81no—
619C4—261no—
620C4—261no—
621C4—261no—
622C4—261no—
623C4—262no—
624C4—522no—
625C4—521no—
626C4—521no—
627C4#1171922711yescharacteristic
628C4C4×Q8×D1311yescharacteristic
629C4D13×C22⋊Q811yescharacteristic
630C4#1171936111yescharacteristic
631C2—21no—
632C2—21no—
633C2—522no—
634C2#1311737011yescharacteristic
635C2#1312374411yescharacteristic
636C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1922C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#1922D13
hypocenterC13#21629
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #13123775C2semidirect
4. #13115778C2semidirect
5. #13115610C2semidirect
6. #13115435C2semidirect
10. #13114719C2semidirect
11. #13114717C2semidirect
12. #13114709C2semidirect
15. C13×#1922C2semidirect
41. #11718552C4semidirect
42. #11718551C4semidirect
43. #11718538C4semidirect
44. #11718536C4semidirect
45. #11718532C4semidirect
46. #11718531C4semidirect
47. #11718518C4semidirect
48. #11718515C4semidirect
84. #88161Q8semidirect
243. #1922D13semidirect
554. C13#21629semidirect

Maximal subgroups

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

subgroupindex
#131246222
#131237752
#131232632
#131157782
#131156102
#131154352
#131151142
#131151102
#131148552
#131147192
#131147172
#131147092
#131146772
#131146722
C13×#19222
#2162913