Finite Group Databasebeta

← #15875242

Subgroups — #15875242

Order 3328.

628 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124618C211yesmaximal, characteristic
2#13123485C211yesmaximal, characteristic
3#13115781C211yesmaximal, characteristic, complemented
4#13115609C211yesmaximal, characteristic, complemented
5#13115586C211yesmaximal, characteristic, complemented
6#13115581C211yesmaximal, characteristic, complemented
7#13115546C211yesmaximal, characteristic
8#13115539C211yesmaximal, characteristic
9#13115484C211yesmaximal, characteristic
10#13115484C211yesmaximal, characteristic
11#13115435C211yesmaximal, characteristic, complemented
12#13115435C211yesmaximal, characteristic, complemented
13#13114853C211yesmaximal, characteristic
14#13114708C211yesmaximal, characteristic, complemented
15C13×#2961C211yesmaximal, characteristic, complemented
16C13×#533C2211yescharacteristic
17C4×#6127C2211yescharacteristic
18C13×#446—21no—
19C13×#446—21no—
20C13×#446—21no—
21C13×#446—21no—
22C13×#424C2211yescharacteristic
23C13×#424C2211yescharacteristic
24C13×#423C2211yescharacteristic
25C13×#405C2211yescharacteristic
26C13×#405C2211yescharacteristic
27C2×C13×#97C2211yescharacteristic
28C2×#88065C2211yescharacteristic
29C2×#88065C2211yescharacteristic
30C2×#88062C2211yescharacteristic
31C2×#88062C2211yescharacteristic
32#11718771C2211yescharacteristic
33#11718771C2211yescharacteristic
34#11718763C2211yescharacteristic
35#11718763C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×C8×Dic13C2211yescharacteristic
38#11718755C411yescharacteristic, complemented
39#11718752C411yescharacteristic, complemented
40#11718748C411yescharacteristic, complemented
41#11718745C411yescharacteristic, complemented
42#11718727C411yescharacteristic, complemented
43#11718727C411yescharacteristic, complemented
44#11718724C411yescharacteristic, complemented
45#11718724C411yescharacteristic, complemented
46#11718663C2211yescharacteristic
47#11718663C2211yescharacteristic
48#11718659C2211yescharacteristic
49#11718659C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C4×#6099C2211yescharacteristic
53#11718370—21no—
54#11718370—21no—
55#11718366—21no—
56#11718366—21no—
57#11718150C2211yescharacteristic
58#11718150C2211yescharacteristic
59#11718147C2211yescharacteristic
60#11718147C2211yescharacteristic
61#11718142C2211yescharacteristic
62#11718142C2211yescharacteristic
63#11718124C2211yescharacteristic
64#11718124C2211yescharacteristic
65#11718124C2211yescharacteristic
66#11718124C2211yescharacteristic
67C2×#6127C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C13×C4⋊Q8C2×C411yescharacteristic
73C13×C4⋊Q8C2×C411yescharacteristic
74C13×#125C2×C411yescharacteristic
75C13×#125C2×C411yescharacteristic
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—21no—
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C13×#117C2311yescharacteristic
81C13×#117C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C4×C22⋊D13—21no—
84C4×C22⋊D13—21no—
85#88180C2311yescharacteristic
86C2×C4⋊Dic13—21no—
87C2×C4×Dic13C2311yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×#6099C2311yescharacteristic
90C2×#6099C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C4×D52C2×C411yescharacteristic
94C4×D52C2×C411yescharacteristic
95#88126—21no—
96C42×D13—21no—
97C4×Dic26C2×C411yescharacteristic
98C4×Dic26C2×C411yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8—21no—
103C13×C4⋊C8—21no—
104C13×C4⋊C8—21no—
105C13×#97—21no—
106C13×#97—21no—
107C13×#97D411yescharacteristic
108C13×#97D411yescharacteristic
109C13×#97D411yescharacteristic
110C13×#97D411yescharacteristic
111C4×C8×C13—21no—
112C4×C8×C13—21no—
113#88071—21no—
114#88065—41no—
115#88065—41no—
116#88062—41no—
117#88062—41no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88060—21no—
122#88055—41no—
123#88054—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127C8×Dic13—41no—
128#88050C2×C411yescharacteristic
129#88050C2×C411yescharacteristic
130#88050C2×C411yescharacteristic
131#88050C2×C411yescharacteristic
132#88049C2×C411yescharacteristic
133#88049C2×C411yescharacteristic
134#88049C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138#88048C2×C411yescharacteristic
139#88048C2×C411yescharacteristic
140#88047C2×C411yescharacteristic
141#88047C2×C411yescharacteristic
142#88047C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144C4⋊#1055C2×C411yescharacteristic
145C4⋊#1055C2×C411yescharacteristic
146C4⋊#1055C2×C411yescharacteristic
147C4⋊#1055C2×C411yescharacteristic
148#88043—21no—
149C4×#1055—21no—
150#22132—131nomaximal, Sylow
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C22×C4×C13#4111yescharacteristic
154C22×C4×C13#4111yescharacteristic
155C22×C4×C13C2411yescharacteristic
156C2×C22⋊D13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159#6127—21no—
160#6127—21no—
161#6127—21no—
162#6127—21no—
163C2×D52C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×Dic26C22×C411yescharacteristic
168C13×M16—21no—
169C13×M16—21no—
170C13×M16—21no—
171C13×M16—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13C2×D411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C2×C8×C13C2×D411yescharacteristic
181C2×C8×C13C2×D411yescharacteristic
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4C22×C411yescharacteristic
189C13×C4⋊C4C22×C411yescharacteristic
190C13×C4⋊C4C22×C411yescharacteristic
191C13×C4⋊C4C22×C411yescharacteristic
192C13×C22⋊C4—21no—
193C13×C22⋊C4—21no—
194C42×C13—21no—
195C42×C13—21no—
196C42×C13C22×C411yescharacteristic
197C42×C13C22×C411yescharacteristic
198C42×C13C2×D411yescharacteristic
199C42×C13C2×D411yescharacteristic
200C22⋊Dic13—21no—
201#6103—21no—
202#6103—21no—
203C4⋊Dic13—42no—
204C4⋊Dic13C22×C411yescharacteristic
205C4⋊Dic13C22×C411yescharacteristic
206#6101—21no—
207#6101—21no—
208C4×Dic13—21no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—21no—
215#6099—21no—
216#6099—21no—
217#6099—21no—
218#6099—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055C22×C411yescharacteristic
226C2×#1055C22×C411yescharacteristic
227C2×#1055C22×C411yescharacteristic
228C2×#1055C22×C411yescharacteristic
229#3076—131no—
230#2961D1311yescharacteristic, complemented
231#2923—131no—
232#1986—131no—
233#1950—131no—
234#1946—131no—
235#1945—131no—
236#1938—131no—
237#1937—131no—
238#1929—131no—
239#1929—131no—
240#1922—131no—
241#1922—131no—
242#1806—131no—
243#1771—131no—
244C23×C13C2×#4111yescharacteristic
245C22×D13—21no—
246Q8×C13—81no—
247Q8×C13—81no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13C4×D411yescharacteristic
255C2×C4×C13C4×D411yescharacteristic
256C2×C4×C13C4×D411yescharacteristic
257C2×C4×C13C4×D411yescharacteristic
258C2×C4×C13C23×C411yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13H(5,𝔽2)11yescharacteristic
261C2×C4×C132−1+411yescharacteristic
262C2×C4×C132−1+411yescharacteristic
263C2×C4×C132−1+411yescharacteristic
264C22⋊D13—41no—
265C22⋊D13—41no—
266C2×Dic13—22no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275D52—21no—
276D52—21no—
277C4×D13—41no—
278C4×D13—41no—
279C4×D13—81no—
280C4×D13—81no—
281Dic26—21no—
282Dic26—21no—
283C8×C13—21no—
284C8×C13—21no—
285C8×C13—21no—
286C8×C13—21no—
287C8×C13—41no—
288C8×C13—41no—
289#1055—21no—
290#1055—21no—
291#1055—21no—
292#1055—21no—
293#1055—41no—
294#1055—41no—
295#533C2×D1311yescharacteristic
296C4×#41—131no—
297#479—131no—
298#479—131no—
299#478—131no—
300#478—131no—
301#477—131no—
302#476—131no—
303#475—131no—
304#474—131no—
305#446—21no—
306#446—21no—
307#446—21no—
308#446—21no—
309#433—261no—
310#433—261no—
311#432—261no—
312#432—261no—
313C2×#108—131no—
314C2×#108—131no—
315#427—131no—
316#427—131no—
317#424—131no—
318#424—131no—
319#424C2×D1311yescharacteristic
320#424C2×D1311yescharacteristic
321#423C2×D1311yescharacteristic
322C2×C4⋊C8—131no—
323C2×#104—131no—
324C2×#104—131no—
325#416—131no—
326#416—131no—
327#408—131no—
328#408—131no—
329#405C2×D1311yescharacteristic
330#405C2×D1311yescharacteristic
331C4×M16—131no—
332C2×#97—131no—
333C2×#97C2×D1311yescharacteristic
334C2×C4×C8—131no—
335C4×C4⋊C4—131no—
336#341—131no—
337#341—131no—
338#339—131no—
339#339—131no—
340#339—131no—
341#339—131no—
342#339—131no—
343#339—131no—
344#336—131no—
345#336—131no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13C2×C4×D411yescharacteristic
349C22×C13#54111yescharacteristic
350C22×C13#54211yescharacteristic
351C2×D13—41no—
352C2×D13—41no—
353C2×D13—41no—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—21no—
357C4×C13—21no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13#51911yescharacteristic
363C4×C13#52011yescharacteristic
364C4×C13#53611yescharacteristic
365C4×C13#53711yescharacteristic
366Dic13—42no—
367Dic13—41no—
368Dic13—41no—
369Dic13—41no—
370Dic13—81no—
371C2×#41—131no—
372C2×M16—131no—
373C2×M16—131no—
374C2×M16C22×D1311yescharacteristic
375C2×M16C22×D1311yescharacteristic
376C22×C8—131no—
377C22×C8—131no—
378C22×C8C22×D1311yescharacteristic
379C22×C8C22×D1311yescharacteristic
380C4⋊Q8C4×D1311yescharacteristic
381C4⋊Q8C4×D1311yescharacteristic
382#125C4×D1311yescharacteristic
383#125C4×D1311yescharacteristic
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—131no—
389C4×Q8—131no—
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—261no—
393C4×D4—261no—
394#117—131no—
395#117—261no—
396#117C22×D1311yescharacteristic
397#117C22×D1311yescharacteristic
398C2×C4⋊C4—261no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—261no—
402C2×C42C22×D1311yescharacteristic
403#108—521no—
404#108—521no—
405#107—131no—
406#107—131no—
407#107—131no—
408#107—131no—
409#106—131no—
410#106—131no—
411#106—131no—
412#106—131no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—131no—
420C4⋊C8—131no—
421C4⋊C8—131no—
422C4⋊C8—131no—
423C4⋊C8—261no—
424C4⋊C8—261no—
425C4⋊C8—261no—
426C4⋊C8—261no—
427#104—521no—
428#104—521no—
429#103—131no—
430#103—131no—
431#103—131no—
432#103—131no—
433#102—131no—
434#102—131no—
435#102—131no—
436#102—131no—
437C22⋊C8—261no—
438C22⋊C8—261no—
439C22⋊C8—261no—
440C22⋊C8—261no—
441#97—21no—
442#97—21no—
443#97—261no—
444#97—521no—
445#97C22⋊D1311yescharacteristic
446#97C22⋊D1311yescharacteristic
447#97C22⋊D1311yescharacteristic
448#97C22⋊D1311yescharacteristic
449C4×C8—21no—
450C4×C8—21no—
451C4×C8—261no—
452C4×C8—521no—
453#95—261no—
454C2×C13—21no—
455C2×C13—21no—
456C2×C13#232311yescharacteristic
457C2×C13#295611yescharacteristic
458C2×C13#295711yescharacteristic
459D13—81no—
460#41—261no—
461#41—261no—
462#41—261no—
463#41—261no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—131no—
467C2×D4—131no—
468C2×D4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4#612711yescharacteristic
475C22×C4#612711yescharacteristic
476C22×C4C23×D1311yescharacteristic
477M16—21no—
478M16—21no—
479M16—21no—
480M16—21no—
481M16—261no—
482M16—261no—
483M16—261no—
484M16—261no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—131no—
492C2×C8—131no—
493C2×C8—131no—
494C2×C8—131no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8C2×C22⋊D1311yescharacteristic
502C2×C8C2×C22⋊D1311yescharacteristic
503C2×C8C2×C22⋊D1311yescharacteristic
504C2×C8C2×C22⋊D1311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—131no—
512C4⋊C4—131no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—522no—
516C4⋊C4C2×C4×D1311yescharacteristic
517C4⋊C4C2×C4×D1311yescharacteristic
518C4⋊C4C2×C4×D1311yescharacteristic
519C4⋊C4C2×C4×D1311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42—21no—
526C42—21no—
527C42—261no—
528C42—261no—
529C42—261no—
530C42—261no—
531C42—261no—
532C42—261no—
533C42—261no—
534C42C2×C4×D1311yescharacteristic
535C42C2×C4×D1311yescharacteristic
536C42C2×C22⋊D1311yescharacteristic
537C42C2×C22⋊D1311yescharacteristic
538C13#2213211yescharacteristic, complemented, Sylow
539C23—261no—
540C23C2×#612711yescharacteristic
541Q8—81no—
542Q8—81no—
543Q8—261no—
544Q8—261no—
545D4—261no—
546D4—261no—
547D4—521no—
548D4—521no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—262no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—1041no—
567C2×C4—1041no—
568C2×C4C4×C22⋊D1311yescharacteristic
569C2×C4C4×C22⋊D1311yescharacteristic
570C2×C4C4×C22⋊D1311yescharacteristic
571C2×C4C4×C22⋊D1311yescharacteristic
572C2×C4C22×C4×D1311yescharacteristic
573C2×C4#8825411yescharacteristic
574C2×C4#8825411yescharacteristic
575C2×C4#8825611yescharacteristic
576C2×C4#8825711yescharacteristic
577C2×C4C22×C22⋊D1311yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—261no—
585C8—261no—
586C8—261no—
587C8—261no—
588C8—521no—
589C8—521no—
590C22—21no—
591C22—21no—
592C22—521no—
593C22—521no—
594C22—521no—
595C22#1171928711yescharacteristic
596C22#1171928811yescharacteristic
597C22C2×C4×C22⋊D1311yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—522no—
607C4—521no—
608C4—521no—
609C4—521no—
610C4—1041no—
611C4#1171927711yescharacteristic
612C4#1171927911yescharacteristic
613C4#1171952111yescharacteristic
614C4#1171953811yescharacteristic
615C2—21no—
616C2—21no—
617C2—1041no—
618C2#1311751211yescharacteristic
619C2#1312374311yescharacteristic
620C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2961C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#2961D13
hypocenterC13#22132
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #13115781C2semidirect
4. #13115609C2semidirect
5. #13115586C2semidirect
6. #13115581C2semidirect
11. #13115435C2semidirect
12. #13115435C2semidirect
14. #13114708C2semidirect
15. C13×#2961C2semidirect
38. #11718755C4semidirect
39. #11718752C4semidirect
40. #11718748C4semidirect
41. #11718745C4semidirect
42. #11718727C4semidirect
43. #11718727C4semidirect
44. #11718724C4semidirect
45. #11718724C4semidirect
230. #2961D13semidirect
538. C13#22132semidirect

Maximal subgroups

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

subgroupindex
#131246182
#131234852
#131157812
#131156092
#131155862
#131155812
#131155462
#131155392
#131154842
#131154352
#131148532
#131147082
C13×#29612
#2213213