Finite Group Databasebeta

← #15833017

Subgroups — #15833017

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124903C211yesmaximal, characteristic
2#13123943C211yesmaximal, characteristic
3#13123927C211yesmaximal, characteristic, complemented
4#13113706C211yesmaximal, characteristic, complemented
5#13113694C211yesmaximal, characteristic, complemented
6#13113689C211yesmaximal, characteristic, complemented
7#13113669C211yesmaximal, characteristic, complemented
8#13113653C211yesmaximal, characteristic, complemented
9#13113648C211yesmaximal, characteristic, complemented
10C8×Dic52C211yesmaximal, characteristic, complemented
11#13113618C211yesmaximal, characteristic, complemented
12#13113267C211yesmaximal, characteristic
13#13113237C211yesmaximal, characteristic, complemented
14#13113135C211yesmaximal, characteristic, complemented
15C8×C13×SD16C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×#6129C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C4×C13×SD16C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718834C411yescharacteristic
22#11718823C411yescharacteristic
23C8×C22⋊D13—21no—
24C2×#88054—21no—
25C4×#6107C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718528C411yescharacteristic
30#11718515C411yescharacteristic
31#11718501—21no—
32#11718496C2211yescharacteristic
33D13×C4⋊C8C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718475C411yescharacteristic
38#11718454C411yescharacteristic
39#11718444C411yescharacteristic
40#11718420C411yescharacteristic
41#11718386—21no—
42#11718379—21no—
43C4×Dic52C2211yescharacteristic
44#11718351—21no—
45#11718346C2211yescharacteristic
46#11718346C2211yescharacteristic
47#11718346C2211yescharacteristic
48#11718340—21no—
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C82×C13C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×#6129C2×C411yescharacteristic
68C2×C13×SD16C2×C411yescharacteristic
69C22×C8×C13—21no—
70C4×Q8×C13C2311yescharacteristic
71C4×D4×C13C2311yescharacteristic
72#88200C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75D4×Dic13C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C4×C22⋊D13—21no—
78C2×C4×Dic13—21no—
79C22×#1055—21no—
80C2×Dic52C2×C411yescharacteristic
81C2×C8×D13—21no—
82#88151C2×C411yescharacteristic
83#88150—21no—
84#88146C2×C411yescharacteristic
85#88143—21no—
86#88142C2×C411yescharacteristic
87#88141C2×C411yescharacteristic
88#88135—21no—
89#88131—21no—
90#88126—21no—
91C42×D13C2311yescharacteristic
92C4×Dic26—21no—
93C4×Dic26C2311yescharacteristic
94C4×Dic26C2311yescharacteristic
95C13×#106C2×C411yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8C2311yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×#103C2×C411yescharacteristic
100C13×#102C2×C411yescharacteristic
101C13×C22⋊C8—21no—
102C4×C8×C13—21no—
103C4×C8×C13C2311yescharacteristic
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88075C2×C411yescharacteristic
107#88072C2×C411yescharacteristic
108C22⋊#1055—21no—
109#88060—21no—
110#88060—21no—
111#88060C2×C411yescharacteristic
112#88060C2×C411yescharacteristic
113#88060D411yescharacteristic
114#88060D411yescharacteristic
115#88058C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117#88056C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054—21no—
125#88054—21no—
126#88054C2×C411yescharacteristic
127#88054C2×C411yescharacteristic
128#88054D411yescharacteristic
129#88054D411yescharacteristic
130C8×Dic13—21no—
131C8×Dic13—21no—
132C8×Dic13—21no—
133#88050C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140#88043—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17921—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13C22×C411yescharacteristic
147C22×C4×C13—21no—
148C2×C22⋊D13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151#6129—22no—
152#6129—22no—
153C2×C4×D13C22×C411yescharacteristic
154C2×C4×D13C2×D411yescharacteristic
155C2×C4×D13#4111yescharacteristic
156C2×Dic26—21no—
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C13×SD16—22no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—81no—
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C22⋊C4—21no—
172C42×C13—21no—
173C42×C13C2411yescharacteristic
174C22⋊Dic13—21no—
175#6107—22no—
176#6105—22no—
177#6103—21no—
178#6103—21no—
179#6103—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13C22×C411yescharacteristic
195C4×Dic13C2×D411yescharacteristic
196C4×Dic13#4111yescharacteristic
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—81no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205Dic52—22no—
206C8×D13—81no—
207#3107—131no—
208#2988—131no—
209#2985—131no—
210#1587—131no—
211#1585—131no—
212#1584—131no—
213#1582—131no—
214#1579—131no—
215SD16⋊C8—131no—
216C8×Q16—131no—
217C8×SD16D1311yescharacteristic, complemented
218#1573—131no—
219#1488—131no—
220#1481—131no—
221#1454—131no—
222C23×C13—21no—
223C22×D13C4×D411yescharacteristic
224Q8×C13—21no—
225Q8×C13—21no—
226D4×C13—21no—
227D4×C13#13112yes—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C22⋊D13—24no—
237C2×Dic13—24no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—81no—
243C2×Dic13C4×D411yescharacteristic
244C2×Dic13C4×D411yescharacteristic
245C2×Dic13C4×D411yescharacteristic
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—21no—
250C4×D13—41no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—81no—
255Dic26#13112yes—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#533—131no—
271C4×#41—131no—
272#485—131no—
273#485—131no—
274#475—131no—
275#474—131no—
276#462—131no—
277#461—131no—
278#452—131no—
279#452—131no—
280#446—131no—
281#446—131no—
282#446—261no—
283#446—261no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8C2×D1311yescharacteristic
288C4×Q16—131no—
289C4×Q16—131no—
290C4×SD16—131no—
291C4×SD16C2×D1311yescharacteristic
292C8×D4—131no—
293C8×D4—261no—
294C8×D4—261no—
295C8×D4C2×D1311yescharacteristic
296#433—261no—
297#433—261no—
298#432—131no—
299#431—131no—
300#431—131no—
301#431—131no—
302#431—261no—
303C2×C4⋊C8—131no—
304C2×C4⋊C8—261no—
305#335—131no—
306#335—131no—
307#334—131no—
308#334C2×D1311yescharacteristic
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8C2×D1311yescharacteristic
315D4⋊C8—131no—
316D4⋊C8C2×D1311yescharacteristic
317#322—131no—
318#322—131no—
319#322—131no—
320C82C2×D1311yescharacteristic
321C22×C13—22no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13C2×C4×D411yescharacteristic
325C2×D13—21no—
326C2×D13—21no—
327C2×D13—21no—
328C4×C13—21no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13C2×#13111yescharacteristic
333C4×C13C2×#13111yescharacteristic
334C4×C13#57711yescharacteristic
335C4×C13#57811yescharacteristic
336Dic13—22no—
337Dic13—21no—
338Dic13—21no—
339Dic13—21no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343C2×#41—131no—
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16C4×D1311yescharacteristic
348C22×C8—21no—
349C22×C8—261no—
350C22×C8—261no—
351C4⋊Q8—131no—
352C4⋊Q8—131no—
353#125—261no—
354C22⋊Q8—131no—
355C22⋊Q8—131no—
356C22⋊Q8—261no—
357C4×Q8—131no—
358C4×Q8—131no—
359C4×Q8—131no—
360C4×Q8—261no—
361C4×Q8C22×D1311yescharacteristic
362C4×D4—131no—
363C4×D4—261no—
364C4×D4—261no—
365C4×D4C22×D1311yescharacteristic
366#117—131no—
367#117—261no—
368#117—261no—
369C2×C42—131no—
370C2×C42—261no—
371#107—131no—
372#107—131no—
373#106—131no—
374#106C4×D1311yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103C4×D1311yescharacteristic
397#102—131no—
398#102C4×D1311yescharacteristic
399C22⋊C8—21no—
400C22⋊C8—131no—
401C22⋊C8—131no—
402C22⋊C8—131no—
403C22⋊C8—131no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—261no—
408#97—261no—
409#97—261no—
410C4×C8—21no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C2×C13—42no—
421C2×C13#292911yescharacteristic
422C2×C13#294711yescharacteristic
423C2×C13#295711yescharacteristic
424D13—41no—
425#41—262no—
426#41—262no—
427C2×Q8—131no—
428C2×Q8—131no—
429C2×Q8—261no—
430C2×Q8C2×C4×D1311yescharacteristic
431C2×D4—261no—
432C2×D4C2×C4×D1311yescharacteristic
433C22×C4—21no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—261no—
438C22×C4—261no—
439Q16—262no—
440Q16—262no—
441SD16—22no—
442SD16—262no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—1041no—
455C2×C8—1041no—
456C2×C8C2×C4×D1311yescharacteristic
457C2×C8C2×C4×D1311yescharacteristic
458C2×C8D4×D1311yescharacteristic
459C2×C8D4×D1311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—131no—
462C4⋊C4—131no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4C2×C4×D1311yescharacteristic
472C4⋊C4C2×C4×D1311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C42—21no—
479C42—131no—
480C42—131no—
481C42—131no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42C23×D1311yescharacteristic
487C13#1792111yescharacteristic, complemented, Sylow
488C23—21no—
489C23—131no—
490Q8—21no—
491Q8—21no—
492Q8—132no—
493Q8—261no—
494Q8—261no—
495Q8—261no—
496Q8—1041no—
497D4—21no—
498D4—264no—
499D4#8815512yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—131no—
508C2×C4—264no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—521no—
518C2×C4—1041no—
519C2×C4C22×C4×D1311yescharacteristic
520C2×C4C2×D4×D1311yescharacteristic
521C2×C4#41×D1311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—261no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—521no—
534C8—521no—
535C8—521no—
536C22—22no—
537C22—41no—
538C22—41no—
539C22—261no—
540C22—261no—
541C22—261no—
542C22C4×D4×D1311yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—261no—
548C4—261no—
549C4—261no—
550C4—262no—
551C4—521no—
552C4—521no—
553C4—521no—
554C4C2×#8815511yescharacteristic
555C4D13×#13111yescharacteristic
556C4#1171946711yescharacteristic
557C4#1171947611yescharacteristic
558C2—42no—
559C2—521no—
560C2#1312352511yescharacteristic
561C2#1312367211yescharacteristic
562C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×SD16C2
socleC22×C13C2×C4×D4
prime radicalC2×#6129C2×C4
cosocleC42×C13C24
hypercenterC8×SD16D13
hypocenterC13#17921
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
3. #13123927C2semidirect
4. #13113706C2semidirect
5. #13113694C2semidirect
6. #13113689C2semidirect
7. #13113669C2semidirect
8. #13113653C2semidirect
9. #13113648C2semidirect
10. C8×Dic52C2semidirect
11. #13113618C2semidirect
13. #13113237C2semidirect
14. #13113135C2semidirect
15. C8×C13×SD16C2semidirect
217. C8×SD16D13semidirect
487. C13#17921semidirect

Maximal subgroups

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

subgroupindex
#131249032
#131239432
#131239272
#131137062
#131136942
#131136892
#131136692
#131136532
#131136482
C8×Dic522
#131136182
#131132672
#131132372
#131131352
C8×C13×SD162
#1792113