Finite Group Databasebeta

← #15834693

Subgroups — #15834693

Order 3328.

586 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125419C211yesmaximal, characteristic
2#13123784C211yesmaximal, characteristic
3#13123778C211yesmaximal, characteristic
4#13113731C211yesmaximal, characteristic, complemented
5#13113730C211yesmaximal, characteristic, complemented
6#13113688C211yesmaximal, characteristic, complemented
7#13113687C211yesmaximal, characteristic, complemented
8#13113685C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11D13×#335C211yesmaximal, characteristic
12#13113237C211yesmaximal, characteristic
13#13113237C211yesmaximal, characteristic
14#13113115C211yesmaximal, characteristic
15C13×#1584C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17#11719283C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718849C411yescharacteristic
22#11718842C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718548C411yescharacteristic
28#11718535C411yescharacteristic
29#11718500—21no—
30#11718500—21no—
31D13×C4⋊C8C2211yescharacteristic
32D13×C4⋊C8C2211yescharacteristic
33#11718492—21no—
34#11718492C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718474C411yescharacteristic
38#11718474C411yescharacteristic
39#11718453C411yescharacteristic
40#11718453C411yescharacteristic
41#11718369—21no—
42#11718362—21no—
43C4×Dic52C2211yescharacteristic
44#11718350—21no—
45C4×#6094C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48#11718340—21no—
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×Q16C2×C411yescharacteristic
68C4×Q8×C13C2311yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70#88200C2×C411yescharacteristic
71#88200C2×C411yescharacteristic
72#88198C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6107C2×C411yescharacteristic
76C2×Dic52C2×C411yescharacteristic
77C2×#6094D411yescharacteristic
78C2×#6094D411yescharacteristic
79C2×C8×D13—21no—
80C2×C8×D13—21no—
81C2×C8×D13C2×C411yescharacteristic
82C2×C8×D13C2×C411yescharacteristic
83#88151C2×C411yescharacteristic
84#88151C2×C411yescharacteristic
85#88150—21no—
86#88150—21no—
87#88143—21no—
88#88143—21no—
89#88142C2×C411yescharacteristic
90#88142C2×C411yescharacteristic
91#88126—21no—
92#88126—21no—
93C42×D13C2311yescharacteristic
94C4×Dic26—21no—
95C4×Dic26—21no—
96C4×Dic26C2311yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×#107C2×C411yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#97—21no—
106C4×C8×C13—21no—
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88075C2×C411yescharacteristic
111#88075C2×C411yescharacteristic
112#88060—21no—
113#88058C2×C411yescharacteristic
114#88056C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88055—21no—
117#88055—21no—
118#88055D411yescharacteristic
119#88055D411yescharacteristic
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127C8×Dic13—21no—
128C8×Dic13—21no—
129C8×Dic13C2×C411yescharacteristic
130C8×Dic13C2×C411yescharacteristic
131#88050C2×C411yescharacteristic
132#88050C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18068—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147C2×C4×D13C22×C411yescharacteristic
148C2×C4×D13C2×D411yescharacteristic
149C2×C4×D13#4111yescharacteristic
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26C22×C411yescharacteristic
153C2×Dic26C22×C411yescharacteristic
154C13×Q16—41no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13C22×C411yescharacteristic
159C2×C8×C13C22×C411yescharacteristic
160C2×C8×C13C2×D411yescharacteristic
161C2×C8×C13C2×D411yescharacteristic
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4C22×C411yescharacteristic
165C13×C4⋊C4C22×C411yescharacteristic
166C42×C13—21no—
167C42×C13—21no—
168C42×C13C2411yescharacteristic
169#6107—22no—
170#6107—22no—
171#6103—21no—
172#6103—21no—
173#6103—21no—
174#6103—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13C22×C411yescharacteristic
178C4⋊Dic13C22×C411yescharacteristic
179#6101—21no—
180#6101—21no—
181#6101—21no—
182#6101—21no—
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13C22×C411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13#4111yescharacteristic
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055C22×C411yescharacteristic
198C2×#1055C22×C411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201Dic52—41no—
202#6094—22no—
203#6094Q1614yescomplemented
204C8×D13—22no—
205C8×D13—41no—
206C8×D13—42no—
207C8×D13—42no—
208#3170—131no—
209#2962—131no—
210#2962—131no—
211#1591—131no—
212#1591—131no—
213#1584—131no—
214#1584—131no—
215#1584—131no—
216#1584D1311yescharacteristic, complemented
217C8×Q16—131no—
218C8×Q16—131no—
219C2×#335—131no—
220#1481—131no—
221#1481—131no—
222C8×M16—131no—
223C22×D13C4×D411yescharacteristic
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13C23×C411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13C4×D411yescharacteristic
240C2×Dic13C4×D411yescharacteristic
241C2×Dic13C4×D411yescharacteristic
242C4×D13—21no—
243C4×D13—21no—
244C4×D13—41no—
245C4×D13C2×Q1612yes—
246C4×D13#13512yes—
247Dic26—21no—
248Dic26—21no—
249Dic26—21no—
250Dic26—21no—
251Dic26—81no—
252Dic26—81no—
253C8×C13—21no—
254C8×C13—21no—
255C8×C13—21no—
256C8×C13—41no—
257C8×C13—41no—
258C8×C13—41no—
259C8×C13C2×Q1612yes—
260#1055—21no—
261#1055—21no—
262#1055—41no—
263#1055—41no—
264#1055—41no—
265#1055#13112yes—
266#1055C2×Q1612yes—
267#533—131no—
268#533—131no—
269#500—131no—
270#494—131no—
271#487—131no—
272#487—131no—
273#467—131no—
274#467—131no—
275#467—131no—
276#467—131no—
277#446—131no—
278#446—131no—
279#446—131no—
280#446—261no—
281#446—261no—
282#446—261no—
283#446—261no—
284#446C2×D1311yescharacteristic
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C4×Q16—131no—
290C4×Q16—131no—
291C4×Q16—131no—
292C4×Q16C2×D1311yescharacteristic
293#431—131no—
294#424—261no—
295#424—261no—
296C2×C4⋊C8—131no—
297C2×C4⋊C8—131no—
298#405—261no—
299#405—261no—
300C4×M16—131no—
301C2×C4×C8—131no—
302#335—131no—
303#335—131no—
304#335—131no—
305#335C2×D1311yescharacteristic
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8C2×D1311yescharacteristic
313Q8⋊C8C2×D1311yescharacteristic
314#322—131no—
315#322C2×D1311yescharacteristic
316C82—131no—
317C82—131no—
318C22×C13C2×C4×D411yescharacteristic
319C2×D13—21no—
320C2×D13—21no—
321C2×D13C4×Q1612yes—
322C4×C13—21no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13C2×#13111yescharacteristic
328C4×C13#56811yescharacteristic
329C4×C13C22×Q1611yescharacteristic
330C4×C13C2×#13511yescharacteristic
331Dic13—21no—
332Dic13—21no—
333Dic13—41no—
334Dic13—41no—
335Dic13—41no—
336Dic13—41no—
337Dic13C4×Q1612yes—
338C2×Q16—131no—
339C2×Q16—131no—
340C2×Q16—131no—
341C2×Q16C4×D1311yescharacteristic
342C2×M16—131no—
343C2×M16—131no—
344C22×C8—131no—
345C22×C8—131no—
346C22×C8—261no—
347C22×C8—261no—
348C4⋊Q8—131no—
349C4⋊Q8—131no—
350C4⋊Q8—131no—
351C4⋊Q8—131no—
352#125—261no—
353#125—261no—
354C22⋊Q8—131no—
355C22⋊Q8—131no—
356C22⋊Q8—131no—
357C22⋊Q8—131no—
358C22⋊Q8—261no—
359C22⋊Q8—261no—
360C4×Q8—131no—
361C4×Q8—131no—
362C4×Q8—261no—
363C4×Q8—261no—
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366#117—261no—
367#117—261no—
368C2×C42—131no—
369#107—131no—
370#107—131no—
371#107—131no—
372#107C4×D1311yescharacteristic
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—131no—
376C4⋊C8—131no—
377C4⋊C8—261no—
378C4⋊C8—261no—
379C4⋊C8—261no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8C22×D1311yescharacteristic
387C4⋊C8C22×D1311yescharacteristic
388#103—131no—
389#103—131no—
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103C4×D1311yescharacteristic
395#103C4×D1311yescharacteristic
396C22⋊C8—261no—
397#97—21no—
398#97—131no—
399#97—131no—
400#97—261no—
401#97—261no—
402#97—261no—
403C4×C8—21no—
404C4×C8—131no—
405C4×C8—131no—
406C4×C8—131no—
407C4×C8—131no—
408C4×C8—131no—
409C4×C8—261no—
410C4×C8—261no—
411C4×C8—261no—
412C4×C8C22×D1311yescharacteristic
413C4×C8C22×D1311yescharacteristic
414C4×C8C22×D1311yescharacteristic
415C2×C13#293511yescharacteristic
416C2×C13C2×C4×Q1611yescharacteristic
417C2×C13#295711yescharacteristic
418D13—22no—
419C2×Q8—131no—
420C2×Q8—131no—
421C2×Q8—261no—
422C2×Q8—261no—
423C2×Q8C2×C4×D1311yescharacteristic
424C2×Q8C2×C4×D1311yescharacteristic
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428Q16—41no—
429Q16—262no—
430Q16—262no—
431Q16—521no—
432M16—134no—
433M16—262no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—131no—
438C2×C8—131no—
439C2×C8—131no—
440C2×C8—131no—
441C2×C8—262no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—521no—
446C2×C8—522no—
447C2×C8—522no—
448C2×C8C2×C4×D1311yescharacteristic
449C2×C8C2×C4×D1311yescharacteristic
450C2×C8D4×D1311yescharacteristic
451C2×C8D4×D1311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—131no—
455C4⋊C4—131no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4C2×C4×D1311yescharacteristic
469C4⋊C4C2×C4×D1311yescharacteristic
470C22⋊C4—261no—
471C22⋊C4—261no—
472C22⋊C4—261no—
473C22⋊C4—261no—
474C42—21no—
475C42—21no—
476C42—131no—
477C42—131no—
478C42—131no—
479C42—261no—
480C42—261no—
481C42C23×D1311yescharacteristic
482C13#1806811yescharacteristic, complemented, Sylow
483C23—131no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—261no—
489Q8—261no—
490Q8—261no—
491Q8—261no—
492Q8—1041no—
493Q8—1041no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—131no—
499C2×C4—132no—
500C2×C4—132no—
501C2×C4—131no—
502C2×C4—131no—
503C2×C4—261no—
504C2×C4—261no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—521no—
510C2×C4C22×C4×D1311yescharacteristic
511C2×C4C2×D4×D1311yescharacteristic
512C2×C4#41×D1311yescharacteristic
513C8—21no—
514C8—21no—
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—132no—
520C8—132no—
521C8—261no—
522C8—261no—
523C8—521no—
524C8—521no—
525C8—521no—
526C8Q16×D1312yes—
527C22—132no—
528C22—261no—
529C22—261no—
530C22C4×D4×D1311yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—132no—
537C4—261no—
538C4—261no—
539C4—521no—
540C4—521no—
541C4—521no—
542C4—521no—
543C4#1171945011yescharacteristic
544C4D13×#13111yescharacteristic
545C4C2×Q16×D1311yescharacteristic
546C4D13×#13511yescharacteristic
547C2—262no—
548C2#1312357711yescharacteristic
549C2C4×Q16×D1311yescharacteristic
550C2#1312375011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1584C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1584D13
hypocenterC13#18068
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13113731C2semidirect
5. #13113730C2semidirect
6. #13113688C2semidirect
7. #13113687C2semidirect
8. #13113685C2semidirect
9. C8×#6107C2semidirect
10. #13113640C2semidirect
15. C13×#1584C2semidirect
203. #6094Q16semidirect
216. #1584D13semidirect
482. C13#18068semidirect

Maximal subgroups

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

subgroupindex
#131254192
#131237842
#131237782
#131137312
#131137302
#131136882
#131136872
#131136852
C8×#61072
#131136402
D13×#3352
#131132372
#131131152
C13×#15842
#1806813