Finite Group Databasebeta

← #15834884

Subgroups — #15834884

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125443C211yesmaximal, characteristic
2#13123996C211yesmaximal, characteristic
3#13123937C211yesmaximal, characteristic, complemented
4#13113742C211yesmaximal, characteristic, complemented
5#13113729C211yesmaximal, characteristic, complemented
6#13113717C211yesmaximal, characteristic, complemented
7#13113704C211yesmaximal, characteristic, complemented
8#13113689C211yesmaximal, characteristic, complemented
9#13113669C211yesmaximal, characteristic, complemented
10#13113645C211yesmaximal, characteristic, complemented
11#13113640C211yesmaximal, characteristic, complemented
12#13113589C211yesmaximal, characteristic, complemented
13#13113240C211yesmaximal, characteristic, complemented
14#13113131C211yesmaximal, characteristic, complemented
15C13×#1482C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718730C411yescharacteristic
21#11718726C411yescharacteristic
22#11718721C411yescharacteristic
23#11718716C411yescharacteristic
24#11718713C411yescharacteristic
25#11718713C411yescharacteristic
26#11718703C411yescharacteristic
27#11718703C411yescharacteristic
28C4×#6107C2211yescharacteristic
29C4×#6107C2211yescharacteristic
30#11718685C2211yescharacteristic
31Q8×#1055C2211yescharacteristic
32C4×#6105C2211yescharacteristic
33C4×#6105C2211yescharacteristic
34#11718673C2211yescharacteristic
35#11718672—21no—
36D4×#1055—21no—
37D4×#1055C2211yescharacteristic
38#11718661—21no—
39#11718660—21no—
40#11718586C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718492C2211yescharacteristic
44#11718492C2211yescharacteristic
45#11718491C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718381—21no—
48#11718381—21no—
49#11718340—21no—
50C8×Dic26—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
67C13×#126—21no—
68C13×#125C2×C411yescharacteristic
69C13×#124C2×C411yescharacteristic
70C13×#123—21no—
71C13×C22⋊Q8C2×C411yescharacteristic
72C13×#121C2×C411yescharacteristic
73C4×Q8×C13C2311yescharacteristic
74C4×D4×C13—21no—
75C4×D4×C13C2311yescharacteristic
76C13×#117—21no—
77C2×C42×C13C2311yescharacteristic
78C2×#6107C2×C411yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6105C2×C411yescharacteristic
81C2×#6105C2×C411yescharacteristic
82#88180—21no—
83#88178—21no—
84#88178C2×C411yescharacteristic
85#88178C2×C411yescharacteristic
86C2×#6099—21no—
87C2×#6099C2×C411yescharacteristic
88C2×#6099C2×C411yescharacteristic
89C22×#1055—21no—
90C22×#1055—21no—
91#88124—21no—
92#88123C2×C411yescharacteristic
93#88123C2×C411yescharacteristic
94C4×Dic26—21no—
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C22⋊C8—21no—
101C13×C22⋊C8—21no—
102C4×C8×C13—21no—
103C4×C8×C13C2311yescharacteristic
104C4×C8×C13C2311yescharacteristic
105#88075C2×C411yescharacteristic
106#88075C2×C411yescharacteristic
107#88072C2×C411yescharacteristic
108#88072C2×C411yescharacteristic
109C22⋊#1055—21no—
110C22⋊#1055—21no—
111C22⋊#1055D411yescharacteristic
112C22⋊#1055D411yescharacteristic
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⋊#1055—21no—
132C4⋊#1055D411yescharacteristic
133C4⋊#1055D411yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136#88043—21no—
137#88043C2×C411yescharacteristic
138#88043C2×C411yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18083—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
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4C22×C411yescharacteristic
164C13×C4⋊C4C22×C411yescharacteristic
165C13×C22⋊C4—21no—
166C13×C22⋊C4—21no—
167C13×C22⋊C4—21no—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C42×C13—21no—
171C42×C13C22×C411yescharacteristic
172C42×C13C2×D411yescharacteristic
173C42×C13#4111yescharacteristic
174C42×C13C2411yescharacteristic
175C22⋊Dic13—21no—
176C22⋊Dic13—21no—
177#6107—22no—
178#6107—41no—
179#6105—22no—
180#6105—41no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13C22×C411yescharacteristic
185C4⋊Dic13C22×C411yescharacteristic
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192#6099—22no—
193#6099—41no—
194#6099—81no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—81no—
198C2×#1055—81no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207#3172—131no—
208#2994—131no—
209#2986—131no—
210#1593—131no—
211#1590—131no—
212#1588—131no—
213#1587—131no—
214#1584—131no—
215#1582—131no—
216SD16⋊C8—131no—
217C8×Q16—131no—
218#1565—131no—
219#1482D1311yescharacteristic
220#1481—131no—
221#1453—131no—
222C23×C13—21no—
223C23×C13C4×D411yescharacteristic
224Q8×C13—21no—
225Q8×C13—21no—
226D4×C13—21no—
227D4×C13—21no—
228D4×C13—42no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C23×C411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249Dic26—21no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—42no—
254C8×C13—41no—
255C8×C13—41no—
256C8×C13—41no—
257C8×C13—41no—
258#1055—21no—
259#1055—21no—
260#1055—21no—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—41no—
266#1055—41no—
267#1055#13112yes—
268#533—131no—
269#529C2×D1311yescharacteristic
270#501—131no—
271#497—131no—
272#491—131no—
273#489—131no—
274#470—131no—
275#470—131no—
276#468—131no—
277#468—131no—
278#446—131no—
279#446—131no—
280#446—131no—
281#446—261no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—261no—
286C4×Q16—131no—
287C4×Q16—131no—
288C4×SD16—131no—
289C4×SD16—131no—
290#436—131no—
291#435—261no—
292C8×D4—131no—
293C8×D4—261no—
294#433—261no—
295#433—261no—
296#433—261no—
297#431—131no—
298#431C2×D1311yescharacteristic
299#431C2×D1311yescharacteristic
300#424—261no—
301C2×C4⋊C8—131no—
302C4×M16—131no—
303#335—131no—
304#335—131no—
305#334—131no—
306#334—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8C2×D1311yescharacteristic
312Q8⋊C8C2×D1311yescharacteristic
313D4⋊C8C2×D1311yescharacteristic
314D4⋊C8C2×D1311yescharacteristic
315#322—131no—
316#322—131no—
317#322—131no—
318C82—131no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13C2×C4×D411yescharacteristic
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13C2×#13111yescharacteristic
334C4×C13#56811yescharacteristic
335C4×C13#57711yescharacteristic
336C4×C13#57811yescharacteristic
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341C2×Q16—131no—
342C2×Q16—131no—
343C2×SD16—131no—
344C2×SD16—131no—
345C2×M16—131no—
346C2×M16—131no—
347C2×M16—261no—
348C22×C8—261no—
349C22×C8—261no—
350C4⋊Q8—131no—
351C4⋊Q8—131no—
352#126—21no—
353#125—261no—
354#125C4×D1311yescharacteristic
355#124C4×D1311yescharacteristic
356#123—21no—
357C22⋊Q8—131no—
358C22⋊Q8—131no—
359C22⋊Q8—261no—
360C22⋊Q8C4×D1311yescharacteristic
361#121C4×D1311yescharacteristic
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—261no—
365C4×Q8C22×D1311yescharacteristic
366C4×D4—21no—
367C4×D4C22×D1311yescharacteristic
368#117—21no—
369#117—261no—
370C2×C42C22×D1311yescharacteristic
371#107—131no—
372#107—131no—
373#106—131no—
374#106—131no—
375C4⋊C8—21no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8C22×D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389#103—131no—
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#102—131no—
396#102—131no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—131no—
400C22⋊C8—131no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—131no—
404#97—131no—
405#97—261no—
406#97—261no—
407#97—261no—
408C4×C8—21no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C2×C13—41no—
419C2×C13—81no—
420C2×C13#293511yescharacteristic
421C2×C13#294711yescharacteristic
422C2×C13#295511yescharacteristic
423C2×Q8—131no—
424C2×Q8—131no—
425C2×Q8—261no—
426C2×Q8C2×C4×D1311yescharacteristic
427C2×D4—21no—
428C2×D4C2×C4×D1311yescharacteristic
429C22×C4—21no—
430C22×C4C2×C4×D1311yescharacteristic
431C22×C4D4×D1311yescharacteristic
432C22×C4#612911yescharacteristic
433Q16—262no—
434Q16—521no—
435SD16—262no—
436SD16—521no—
437M16—262no—
438M16—521no—
439M16—1041no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—131no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—1041no—
455C2×C8—1041no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—131no—
461C4⋊C4—131no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4C2×C4×D1311yescharacteristic
470C4⋊C4C2×C4×D1311yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C42—21no—
479C42—261no—
480C42—261no—
481C42C2×C4×D1311yescharacteristic
482C42D4×D1311yescharacteristic
483C42#612911yescharacteristic
484C42C23×D1311yescharacteristic
485C13#1808311yescharacteristic, complemented, Sylow
486C23—21no—
487C23#8813511yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—261no—
491Q8—261no—
492Q8—261no—
493Q8—261no—
494Q8—522no—
495D4—21no—
496D4—21no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4#8813511yescharacteristic
513C2×C4#8813511yescharacteristic
514C2×C4#8813511yescharacteristic
515C2×C4C22×C4×D1311yescharacteristic
516C2×C4C2×D4×D1311yescharacteristic
517C2×C4C2×#612911yescharacteristic
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—132no—
523C8—261no—
524C8—261no—
525C8—261no—
526C8—261no—
527C8—261no—
528C8—261no—
529C8—261no—
530C8—521no—
531C8—521no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#8813511yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—521no—
547C4—521no—
548C4—521no—
549C4—521no—
550C4D13×#13111yescharacteristic
551C4#1171945511yescharacteristic
552C4#1171947511yescharacteristic
553C4#1171947611yescharacteristic
554C2—41no—
555C2—81no—
556C2#1312357611yescharacteristic
557C2#1312368211yescharacteristic
558C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1482C2
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC42×C13C24
hypercenter#1482D13
hypocenterC13#18083
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
3. #13123937C2semidirect
4. #13113742C2semidirect
5. #13113729C2semidirect
6. #13113717C2semidirect
7. #13113704C2semidirect
8. #13113689C2semidirect
9. #13113669C2semidirect
10. #13113645C2semidirect
11. #13113640C2semidirect
12. #13113589C2semidirect
13. #13113240C2semidirect
14. #13113131C2semidirect
485. C13#18083semidirect

Maximal subgroups

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

subgroupindex
#131254432
#131239962
#131239372
#131137422
#131137292
#131137172
#131137042
#131136892
#131136692
#131136452
#131136402
#131135892
#131132402
#131131312
C13×#14822
#1808313