Finite Group Databasebeta

← #15834848

Subgroups — #15834848

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#13125436C211yesmaximal, characteristic
2#13123998C211yesmaximal, characteristic
3#13113736C211yesmaximal, characteristic, complemented
4#13113731C211yesmaximal, characteristic, complemented
5#13113707C211yesmaximal, characteristic, complemented
6#13113691C211yesmaximal, characteristic, complemented
7#13113684C211yesmaximal, characteristic, complemented
8#13113679C211yesmaximal, characteristic, complemented
9#13113653C211yesmaximal, characteristic, complemented
10C8×#6106C211yesmaximal, characteristic, complemented
11#13113589C211yesmaximal, characteristic, complemented
12#13113242C211yesmaximal, characteristic
13#13113239C211yesmaximal, characteristic, complemented
14#13113131C211yesmaximal, characteristic, complemented
15C13×#2986C211yesmaximal, characteristic, complemented
16C13×#533C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#446—21no—
19C13×#446C2211yescharacteristic
20C13×#446C2211yescharacteristic
21C8×Q8×C13—21no—
22C8×Q8×C13C2211yescharacteristic
23C8×Q8×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#433—21no—
26C13×#431C2211yescharacteristic
27C13×#431C2211yescharacteristic
28#11718750C411yescharacteristic
29#11718747C411yescharacteristic
30#11718743C411yescharacteristic
31#11718741C411yescharacteristic
32#11718713C411yescharacteristic
33#11718713C411yescharacteristic
34#11718710C411yescharacteristic
35#11718710C411yescharacteristic
36C4×#6107C2211yescharacteristic
37C4×#6107C2211yescharacteristic
38C4×#6106C2211yescharacteristic
39C4×#6106C2211yescharacteristic
40#11718586C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718501—21no—
44#11718500—21no—
45#11718391—21no—
46#11718386—21no—
47#11718349C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C13×C4⋊Q8C2×C411yescharacteristic
68C13×C4⋊Q8C2×C411yescharacteristic
69C13×#125—21no—
70C13×C22⋊Q8—21no—
71C13×C22⋊Q8C2×C411yescharacteristic
72C13×C22⋊Q8C2×C411yescharacteristic
73C4×Q8×C13—21no—
74C4×Q8×C13C2311yescharacteristic
75C4×Q8×C13C2311yescharacteristic
76C13×#117—21no—
77C2×C42×C13C2311yescharacteristic
78C2×#6107C2×C411yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6106C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82#88184C2×C411yescharacteristic
83#88183—21no—
84C4×C22⋊D13—21no—
85#88178C2×C411yescharacteristic
86C2×#6099C2×C411yescharacteristic
87C2×#6099C2×C411yescharacteristic
88C22×#1055—21no—
89C2×#6094—21no—
90C2×C8×D13—21no—
91#88130—21no—
92#88129C2×C411yescharacteristic
93C4×D52C2311yescharacteristic
94#88126—21no—
95#88124C2×C411yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8—21no—
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8D411yescharacteristic
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8D411yescharacteristic
107C13×C22⋊C8D411yescharacteristic
108C13×#97—21no—
109C13×#97—21no—
110C4×C8×C13—21no—
111C4×C8×C13—21no—
112C4×C8×C13—21no—
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115#88075C2×C411yescharacteristic
116#88075C2×C411yescharacteristic
117#88075C2×C411yescharacteristic
118#88075C2×C411yescharacteristic
119C22⋊#1055—21no—
120#88060—21no—
121#88060—21no—
122#88055—21no—
123#88054—21no—
124#88054—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055C2311yescharacteristic
137C4⋊#1055C2311yescharacteristic
138#88043C2×C411yescharacteristic
139#88043C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18081—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13#4111yescharacteristic
151C2×C22⋊D13—21no—
152C2×D52C22×C411yescharacteristic
153C2×C4×D13—21no—
154C2×Dic26C22×C411yescharacteristic
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13C2×D411yescharacteristic
158C2×C8×C13C2×D411yescharacteristic
159C2×C8×C13C2×D411yescharacteristic
160C2×C8×C13C2×D411yescharacteristic
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C22⋊C4—21no—
171C13×C22⋊C4—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13C22×C411yescharacteristic
175C42×C13C2×D411yescharacteristic
176C42×C13#4111yescharacteristic
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179#6107—22no—
180#6107—41no—
181#6106—22no—
182#6106—41no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193C4×Dic13—21no—
194#6099—22no—
195#6099—41no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—81no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205#6094—81no—
206C8×D13—81no—
207#3172—131no—
208#2994—131no—
209#2986D1311yescharacteristic, complemented
210#1592—131no—
211#1591—131no—
212#1587—131no—
213#1585—131no—
214#1584—131no—
215#1583—131no—
216#1579—131no—
217C8×SD16—131no—
218#1565—131no—
219#1482—131no—
220#1481—131no—
221#1453—131no—
222C23×C13C4×D411yescharacteristic
223C22×D13—21no—
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×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—21no—
237C2×C4×C13—41no—
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C22⋊D13—42no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248D52—21no—
249D52—21no—
250C4×D13—41no—
251C4×D13—41no—
252Dic26—21no—
253Dic26—21no—
254C8×C13—21no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—41no—
259C8×C13—41no—
260#1055—21no—
261#1055—21no—
262#1055—21no—
263#1055—41no—
264#1055—41no—
265#1055—41no—
266#1055—41no—
267#1055#13112yes—
268#533C2×D1311yescharacteristic
269#529—131no—
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—21no—
279#446—131no—
280#446C2×D1311yescharacteristic
281#446C2×D1311yescharacteristic
282C8×Q8—21no—
283C8×Q8—131no—
284C8×Q8C2×D1311yescharacteristic
285C8×Q8C2×D1311yescharacteristic
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—21no—
295#433—21no—
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⋊C8—131no—
312Q8⋊C8—131no—
313D4⋊C8—131no—
314D4⋊C8—131no—
315#322—131no—
316#322—131no—
317#322—131no—
318C82—131no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13C2×C4×D411yescharacteristic
323C2×D13—41no—
324C2×D13—41no—
325C2×D13—41no—
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13C2×#13111yescharacteristic
335C4×C13#56811yescharacteristic
336C4×C13#57711yescharacteristic
337C4×C13#57811yescharacteristic
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⋊Q8C4×D1311yescharacteristic
351C4⋊Q8C4×D1311yescharacteristic
352#126—261no—
353#125—21no—
354#125—131no—
355#124—131no—
356#123—261no—
357C22⋊Q8—21no—
358C22⋊Q8—131no—
359C22⋊Q8C4×D1311yescharacteristic
360C22⋊Q8C4×D1311yescharacteristic
361#121—131no—
362C4×Q8—21no—
363C4×Q8—131no—
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—131no—
367C4×D4—261no—
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—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8C22⋊D1311yescharacteristic
386C4⋊C8C22⋊D1311yescharacteristic
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—261no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8C22⋊D1311yescharacteristic
402C22⋊C8C22⋊D1311yescharacteristic
403#97—21no—
404#97—21no—
405#97—131no—
406#97—131no—
407#97—261no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—261no—
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C2×C13—41no—
419C2×C13#293511yescharacteristic
420C2×C13#294711yescharacteristic
421C2×C13#295511yescharacteristic
422D13—81no—
423C2×Q8—21no—
424C2×Q8—131no—
425C2×Q8C2×C4×D1311yescharacteristic
426C2×Q8C2×C4×D1311yescharacteristic
427C2×D4—131no—
428C2×D4—261no—
429C22×C4—261no—
430C22×C4C2×C4×D1311yescharacteristic
431C22×C4#612711yescharacteristic
432C22×C4C2×C22⋊D1311yescharacteristic
433Q16—262no—
434Q16—521no—
435SD16—262no—
436SD16—521no—
437M16—262no—
438M16—521no—
439M16—1041no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—131no—
443C2×C8—131no—
444C2×C8—131no—
445C2×C8—131no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—1041no—
451C2×C8—1041no—
452C2×C8C2×C22⋊D1311yescharacteristic
453C2×C8C2×C22⋊D1311yescharacteristic
454C2×C8C2×C22⋊D1311yescharacteristic
455C2×C8C2×C22⋊D1311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—131no—
464C4⋊C4—131no—
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—261no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C42—21no—
479C42—21no—
480C42—261no—
481C42C2×C4×D1311yescharacteristic
482C42#612711yescharacteristic
483C42C2×C22⋊D1311yescharacteristic
484C42C23×D1311yescharacteristic
485C13#1808111yescharacteristic, complemented, Sylow
486C23—261no—
487C23C4×C22⋊D1311yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—42no—
493Q8—261no—
494Q8—261no—
495D4—261no—
496D4—261no—
497D4—522no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—521no—
511C2×C4—521no—
512C2×C4C4×C22⋊D1311yescharacteristic
513C2×C4C4×C22⋊D1311yescharacteristic
514C2×C4C4×C22⋊D1311yescharacteristic
515C2×C4C22×C4×D1311yescharacteristic
516C2×C4C2×#612711yescharacteristic
517C2×C4C22×C22⋊D1311yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—132no—
525C8—261no—
526C8—261no—
527C8—261no—
528C8—521no—
529C8—521no—
530C8—521no—
531C8—521no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—521no—
536C22—521no—
537C22—521no—
538C22C2×C4×C22⋊D1311yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—521no—
548C4—521no—
549C4—521no—
550C4D13×#13111yescharacteristic
551C4#1171945511yescharacteristic
552C4#1171954211yescharacteristic
553C4#1171954311yescharacteristic
554C2—41no—
555C2—1041no—
556C2#1312357811yescharacteristic
557C2#1312367911yescharacteristic
558C2#1312373711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2986C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#2986D13
hypocenterC13#18081
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2986

Complements

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

NH ≅ G/Ntype
3. #13113736C2semidirect
4. #13113731C2semidirect
5. #13113707C2semidirect
6. #13113691C2semidirect
7. #13113684C2semidirect
8. #13113679C2semidirect
9. #13113653C2semidirect
10. C8×#6106C2semidirect
11. #13113589C2semidirect
13. #13113239C2semidirect
14. #13113131C2semidirect
15. C13×#2986C2semidirect
209. #2986D13semidirect
485. C13#18081semidirect

Maximal subgroups

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

subgroupindex
#131254362
#131239982
#131137362
#131137312
#131137072
#131136912
#131136842
#131136792
#131136532
C8×#61062
#131135892
#131132422
#131132392
#131131312
C13×#29862
#1808113