Finite Group Databasebeta

← #15834824

Subgroups — #15834824

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125443C211yesmaximal, characteristic
2#13123841C211yesmaximal, characteristic
3#13123779C211yesmaximal, characteristic, complemented
4#13113742C211yesmaximal, characteristic, complemented
5#13113729C211yesmaximal, characteristic, complemented
6#13113710C211yesmaximal, characteristic, complemented
7#13113690C211yesmaximal, characteristic, complemented
8#13113683C211yesmaximal, characteristic, complemented
9#13113682C211yesmaximal, characteristic, complemented
10#13113645C211yesmaximal, characteristic, complemented
11#13113640C211yesmaximal, characteristic, complemented
12#13113586C211yesmaximal, characteristic, complemented
13#13113258C211yesmaximal, characteristic, complemented
14#13113139C211yesmaximal, characteristic, complemented
15C13×#1483C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17#11719175C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C4×C13×M16C2211yescharacteristic
20#11718763—21no—
21#11718762—21no—
22#11718730C411yescharacteristic
23#11718726C411yescharacteristic
24#11718721C411yescharacteristic
25#11718716C411yescharacteristic
26#11718713C411yescharacteristic
27#11718713C411yescharacteristic
28#11718703C411yescharacteristic
29#11718703C411yescharacteristic
30C4×#6107C2211yescharacteristic
31C4×#6107C2211yescharacteristic
32#11718685C2211yescharacteristic
33Q8×#1055C2211yescharacteristic
34C4×#6105C2211yescharacteristic
35C4×#6105C2211yescharacteristic
36#11718673—21no—
37#11718673C2211yescharacteristic
38#11718672—21no—
39D4×#1055C2211yescharacteristic
40#11718661—21no—
41#11718658—21no—
42#11718586C2211yescharacteristic
43C4×#6099C2211yescharacteristic
44C4×#6099C2211yescharacteristic
45#11718492C2211yescharacteristic
46#11718492C2211yescharacteristic
47#11718491C2211yescharacteristic
48#11718491C2211yescharacteristic
49#11718489—21no—
50#11718489—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718048C2211yescharacteristic
60#11718048C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×M16—21no—
68C22×C8×C13—21no—
69C13×#126—21no—
70C13×#125C2×C411yescharacteristic
71C13×#124C2×C411yescharacteristic
72C13×#123—21no—
73C13×C22⋊Q8C2×C411yescharacteristic
74C13×#121C2×C411yescharacteristic
75C4×Q8×C13C2311yescharacteristic
76C4×D4×C13—21no—
77C4×D4×C13C2311yescharacteristic
78C13×#117—21no—
79C2×C42×C13C2311yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6107C2×C411yescharacteristic
82C2×#6105C2×C411yescharacteristic
83C2×#6105C2×C411yescharacteristic
84#88180—21no—
85#88178—21no—
86#88178C2×C411yescharacteristic
87#88178C2×C411yescharacteristic
88C2×#6099—21no—
89C2×#6099C2×C411yescharacteristic
90C2×#6099C2×C411yescharacteristic
91C2×#6099D411yescharacteristic
92C2×#6099D411yescharacteristic
93C22×#1055—21no—
94#88124—21no—
95#88123C2×C411yescharacteristic
96#88123C2×C411yescharacteristic
97C4×Dic26—21no—
98C4×Dic26C2311yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×#97—21no—
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88075C2×C411yescharacteristic
107#88075C2×C411yescharacteristic
108#88072C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110C22⋊#1055—21no—
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113#88055—21no—
114#88055—21no—
115#88054—21no—
116#88054—21no—
117#88054—21no—
118#88054—21no—
119C8×Dic13—21no—
120C8×Dic13—21no—
121#88050C2×C411yescharacteristic
122#88050C2×C411yescharacteristic
123#88050C2×C411yescharacteristic
124#88050C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055C2311yescharacteristic
132C4⋊#1055C2311yescharacteristic
133#88043—21no—
134#88043C2×C411yescharacteristic
135#88043C2×C411yescharacteristic
136#88043D411yescharacteristic
137#88043D411yescharacteristic
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18079—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C2×Dic26—21no—
153C2×Dic26C22×C411yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155C13×M16—42no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—42no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4C22×C411yescharacteristic
166C13×C4⋊C4C22×C411yescharacteristic
167C13×C22⋊C4—21no—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C13×C22⋊C4—21no—
171C13×C22⋊C4—21no—
172C42×C13—21no—
173C42×C13C22×C411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C42×C13#4111yescharacteristic
176C42×C13C2411yescharacteristic
177C22⋊Dic13—21no—
178C22⋊Dic13—21no—
179#6107—22no—
180#6107—41no—
181#6105—22no—
182#6105—41no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194#6099—22no—
195#6099—22no—
196#6099—41no—
197#6099—41no—
198#6099—42no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—42no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210#3172—131no—
211#2969—131no—
212#2962—131no—
213#1593—131no—
214#1590—131no—
215#1587—131no—
216#1585—131no—
217#1584—131no—
218#1583—131no—
219SD16⋊C8—131no—
220C8×Q16—131no—
221#1565—131no—
222#1485—131no—
223#1483D1311yescharacteristic
224#1455—131no—
225C23×C13—21no—
226C23×C13C4×D411yescharacteristic
227Q8×C13—21no—
228Q8×C13—21no—
229D4×C13—21no—
230D4×C13—21no—
231D4×C13—81no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C23×C411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—81no—
257C8×C13—22no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—41no—
268#1055—41no—
269#1055#13112yes—
270#1055#13712yes—
271#533—131no—
272#529C2×D1311yescharacteristic
273#501—131no—
274#497—131no—
275#491—131no—
276#489—131no—
277#470—131no—
278#470—131no—
279#468—131no—
280#468—131no—
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293#436—131no—
294#436—261no—
295#435—261no—
296C8×D4—131no—
297#433—261no—
298#431—131no—
299#424—261no—
300C2×C4⋊C8C2×D1311yescharacteristic
301#405—261no—
302#405—261no—
303C4×M16—131no—
304C4×M16—131no—
305C4×M16C2×D1311yescharacteristic
306#335—131no—
307#335—131no—
308#334—131no—
309#334—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8C2×D1311yescharacteristic
315Q8⋊C8C2×D1311yescharacteristic
316D4⋊C8C2×D1311yescharacteristic
317D4⋊C8C2×D1311yescharacteristic
318#322—131no—
319#322—131no—
320#322—131no—
321C82—131no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13C2×C4×D411yescharacteristic
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13C2×#13111yescharacteristic
337C4×C13#56811yescharacteristic
338C4×C13C2×#13711yescharacteristic
339C4×C13#57511yescharacteristic
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16—131no—
348C2×M16—21no—
349C2×M16—131no—
350C2×M16—131no—
351C2×M16—131no—
352C2×M16—131no—
353C2×M16—261no—
354C22×C8—21no—
355C22×C8—261no—
356C4⋊Q8—131no—
357C4⋊Q8—131no—
358#126—21no—
359#125—261no—
360#125C4×D1311yescharacteristic
361#124C4×D1311yescharacteristic
362#123—21no—
363C22⋊Q8—131no—
364C22⋊Q8—131no—
365C22⋊Q8—261no—
366C22⋊Q8C4×D1311yescharacteristic
367#121C4×D1311yescharacteristic
368C4×Q8—131no—
369C4×Q8—131no—
370C4×Q8—261no—
371C4×Q8C22×D1311yescharacteristic
372C4×D4—21no—
373C4×D4C22×D1311yescharacteristic
374#117—21no—
375#117—261no—
376C2×C42C22×D1311yescharacteristic
377#107—131no—
378#107—131no—
379#106—131no—
380#106—131no—
381C4⋊C8—21no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8C22×D1311yescharacteristic
391C4⋊C8C22×D1311yescharacteristic
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—21no—
404#97—131no—
405#97—131no—
406#97—131no—
407#97—131no—
408#97—261no—
409#97—261no—
410#97—261no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—41no—
422C2×C13—81no—
423C2×C13#293511yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13#295611yescharacteristic
426C2×Q8—131no—
427C2×Q8—131no—
428C2×Q8—261no—
429C2×Q8C2×C4×D1311yescharacteristic
430C2×D4—21no—
431C2×D4C2×C4×D1311yescharacteristic
432C22×C4—21no—
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4D4×D1311yescharacteristic
435C22×C4#612911yescharacteristic
436Q16—262no—
437Q16—521no—
438SD16—262no—
439SD16—521no—
440M16—42no—
441M16—262no—
442M16—262no—
443M16—522no—
444M16—521no—
445M16—521no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—522no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—131no—
467C4⋊C4—131no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4C2×C4×D1311yescharacteristic
476C4⋊C4C2×C4×D1311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—21no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42D4×D1311yescharacteristic
489C42#612911yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1807911yescharacteristic, complemented, Sylow
492C23—21no—
493C23#8813511yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—261no—
497Q8—261no—
498Q8—261no—
499Q8—261no—
500Q8—1041no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4#8813511yescharacteristic
519C2×C4#8813511yescharacteristic
520C2×C4#8813511yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4C2×#612911yescharacteristic
524C8—22no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—132no—
529C8—132no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—521no—
537C8—521no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C2×#8813511yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—521no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4D13×#13111yescharacteristic
557C4#1171945511yescharacteristic
558C4#1171947811yescharacteristic
559C4D13×#13711yescharacteristic
560C2—41no—
561C2—81no—
562C2#1312357611yescharacteristic
563C2#1312366011yescharacteristic
564C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1483C2
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC42×C13C24
hypercenter#1483D13
hypocenterC13#18079
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
3. #13123779C2semidirect
4. #13113742C2semidirect
5. #13113729C2semidirect
6. #13113710C2semidirect
7. #13113690C2semidirect
8. #13113683C2semidirect
9. #13113682C2semidirect
10. #13113645C2semidirect
11. #13113640C2semidirect
12. #13113586C2semidirect
13. #13113258C2semidirect
14. #13113139C2semidirect
491. C13#18079semidirect

Maximal subgroups

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

subgroupindex
#131254432
#131238412
#131237792
#131137422
#131137292
#131137102
#131136902
#131136832
#131136822
#131136452
#131136402
#131135862
#131132582
#131131392
C13×#14832
#1807913