Finite Group Databasebeta

← #15867336

Subgroups — #15867336

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123634C211yesmaximal, characteristic
2#13123478C211yesmaximal, characteristic, complemented
3#13115728C211yesmaximal, characteristic
4#13115723C211yesmaximal, characteristic
5#13115586C211yesmaximal, characteristic, complemented
6#13115581C211yesmaximal, characteristic, complemented
7#13115550C211yesmaximal, characteristic, complemented
8#13115546C211yesmaximal, characteristic, complemented
9#13115543C211yesmaximal, characteristic, complemented
10#13115539C211yesmaximal, characteristic, complemented
11#13114743C211yesmaximal, characteristic, complemented
12#13114649C211yesmaximal, characteristic, complemented
13#13114646C211yesmaximal, characteristic, complemented
14#13114522C211yesmaximal, characteristic, complemented
15C13×#2922C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17C2×#88204C2211yescharacteristic
18C4×#6127C2211yescharacteristic
19C13×#433—22no—
20C13×#431—22no—
21C13×#424C2211yescharacteristic
22C13×#424C2211yescharacteristic
23C13×#408C2211yescharacteristic
24C13×#408C2211yescharacteristic
25C4×C13×M16C2211yescharacteristic
26C2×C4×C8×C13C2211yescharacteristic
27C2×#88077C2211yescharacteristic
28C2×#88077C2211yescharacteristic
29#11718894C2211yescharacteristic
30C2×#88065C2211yescharacteristic
31C2×#88065C2211yescharacteristic
32C2×#88062C2211yescharacteristic
33C2×#88062C2211yescharacteristic
34#11718771C2211yescharacteristic
35#11718771C2211yescharacteristic
36#11718763C2211yescharacteristic
37#11718763C2211yescharacteristic
38C2×#88055C2211yescharacteristic
39C2×#88055C2211yescharacteristic
40C2×C8×Dic13C2211yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42#11718691C412yescomplemented
43#11718687C412yescomplemented
44#11718679C412yescomplemented
45#11718675C412yescomplemented
46#11718663C2211yescharacteristic
47#11718659C2211yescharacteristic
48#11718593C2211yescharacteristic
49C4×#6099C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718351—22no—
52#11718346—22no—
53#11718150C2211yescharacteristic
54#11718150C2211yescharacteristic
55#11718147C2211yescharacteristic
56#11718147C2211yescharacteristic
57#11718124C2211yescharacteristic
58#11718124C2211yescharacteristic
59C2×C13×#41C2311yescharacteristic
60C2×#6127C2311yescharacteristic
61C2×C13×M16C2311yescharacteristic
62C2×C13×M16C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C4×Q8×C13C2×C412yes—
66C4×D4×C13—22no—
67C4×D4×C13C2×C412yes—
68C13×#117—21no—
69C13×#117C2311yescharacteristic
70C2×C42×C13—21no—
71C2×C42×C13C2311yescharacteristic
72#88204—22no—
73#88204—22no—
74C2×#6107C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C2×#6104C2×C411yescharacteristic
78C4×C22⋊D13—22no—
79#88180C2311yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×#6099C2311yescharacteristic
83C2×#6099C2311yescharacteristic
84C22×#1055C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C4×D52C2×C412yes—
87#88126—21no—
88C42×D13—21no—
89C4×Dic26C2×C412yes—
90C13×C4⋊C8—22no—
91C13×C4⋊C8—22no—
92C13×C22⋊C8—22no—
93C13×C22⋊C8—22no—
94C13×#97—21no—
95C4×C8×C13—21no—
96C4×C8×C13D412yes—
97C4×C8×C13D412yes—
98#88077—22no—
99#88077—22no—
100#88075C2×C412yes—
101#88072C2×C412yes—
102#88071—22no—
103#88065—22no—
104#88065—22no—
105#88062—22no—
106#88062—22no—
107#88060—22no—
108#88060—22no—
109#88055—22no—
110#88055—22no—
111#88054—22no—
112#88054—22no—
113C8×Dic13—22no—
114C8×Dic13—22no—
115#88050C2×C412yes—
116#88049C2×C412yes—
117#88048C2×C412yes—
118#88047C2×C412yes—
119#88043—21no—
120#88043C2×C412yes—
121#88043C2×C412yes—
122C4×#1055—21no—
123#21296—131nomaximal, Sylow
124C13×#41—21no—
125C13×#41—21no—
126C13×#41—21no—
127C13×#41—21no—
128C2×Q8×C13C22×C411yescharacteristic
129C2×D4×C13—21no—
130C2×D4×C13C22×C411yescharacteristic
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13#4112yes—
134C22×C4×C13C2411yescharacteristic
135C2×C22⋊D13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138#6127—21no—
139#6127—21no—
140#6127—21no—
141#6127—21no—
142C2×D52C22×C411yescharacteristic
143C2×C4×D13—22no—
144C2×C4×D13—21no—
145C2×Dic26C22×C411yescharacteristic
146C13×M16—21no—
147C13×M16—21no—
148C13×M16—21no—
149C13×M16—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13C2×D412yes—
157C2×C8×C13C2×D412yes—
158C13×C4⋊C4—22no—
159C13×C4⋊C4C22×C412yes—
160C13×C22⋊C4—21no—
161C13×C22⋊C4—22no—
162C42×C13—22no—
163C42×C13—21no—
164C42×C13C22×C412yes—
165C42×C13C2×D411yescharacteristic
166C42×C13C2×D411yescharacteristic
167C22⋊Dic13—21no—
168#6107—22no—
169#6106—22no—
170#6105—22no—
171#6104—22no—
172#6103—22no—
173C4⋊Dic13C22×C412yes—
174#6101—22no—
175C4×Dic13—22no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—21no—
179C4×Dic13#4112yes—
180C4×Dic13#4112yes—
181#6099—21no—
182#6099—21no—
183#6099—21no—
184#6099—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055C22×C412yes—
190C2×#1055C22×C411yescharacteristic
191C2×#1055C22×C411yescharacteristic
192C2×#1055#4112yes—
193C2×#1055#4112yes—
194#2943—131no—
195#2922—131no—
196#2922D1311yescharacteristic, complemented
197#1975—131no—
198#1974—131no—
199#1946—131no—
200#1945—131no—
201#1938—131no—
202#1938—131no—
203#1937—131no—
204#1937—131no—
205#1778—131no—
206#1759—131no—
207#1759—131no—
208#1726—131no—
209C23×C13—21no—
210C23×C13C2×#4111yescharacteristic
211C22×D13—21no—
212Q8×C13—21no—
213Q8×C13—21no—
214D4×C13—21no—
215D4×C13—21no—
216D4×C13—41no—
217D4×C13—41no—
218C2×C4×C13—22no—
219C2×C4×C13—21no—
220C2×C4×C13—42no—
221C2×C4×C13—44no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13C4×D412yes—
225C2×C4×C13C4×D412yes—
226C2×C4×C13C23×C411yescharacteristic
227C2×C4×C13C22×D411yescharacteristic
228C2×C4×C13C2×#4111yescharacteristic
229C2×C4×C13C2×#4111yescharacteristic
230C2×C4×C13C2×#4111yescharacteristic
231C2×C4×C13C2×#4111yescharacteristic
232C22⋊D13—41no—
233C22⋊D13—41no—
234C2×Dic13—21no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240D52—21no—
241D52—21no—
242C4×D13—44no—
243C4×D13—41no—
244C4×D13—41no—
245Dic26—21no—
246Dic26—21no—
247C8×C13—22no—
248C8×C13—22no—
249C8×C13—41no—
250C8×C13—41no—
251#1055—22no—
252#1055—41no—
253#1055—41no—
254#1055#11712yes—
255#1055#11712yes—
256C2×#135—131no—
257C4×#41—131no—
258C4×#41C2×D1311yescharacteristic
259#442—132no—
260#441—132no—
261#440—132no—
262#440—132no—
263#433—22no—
264#433—262no—
265#431—22no—
266#431—262no—
267C2×#108—131no—
268C2×#108—131no—
269#427—131no—
270#424—131no—
271#424—131no—
272#424C2×D1311yescharacteristic
273#424C2×D1311yescharacteristic
274C2×#104—131no—
275C2×#104—131no—
276C2×#104—131no—
277C2×#104—131no—
278#416—131no—
279#416—131no—
280#408—131no—
281#408—131no—
282#408C2×D1311yescharacteristic
283#408C2×D1311yescharacteristic
284C4×M16—131no—
285C4×M16C2×D1311yescharacteristic
286C2×#97—131no—
287C2×#97—131no—
288C2×#97—131no—
289C2×C4×C8—131no—
290C2×C4×C8—131no—
291C2×C4×C8C2×D1311yescharacteristic
292#376—131no—
293#341—131no—
294#341—131no—
295#339—131no—
296#339—131no—
297#339—131no—
298#339—131no—
299C22×C13—22no—
300C22×C13—42no—
301C22×C13—41no—
302C22×C13C2×C4×D411yescharacteristic
303C22×C13#52911yescharacteristic
304C22×C13#52911yescharacteristic
305C2×D13—42no—
306C2×D13—41no—
307C4×C13—22no—
308C4×C13—22no—
309C4×C13—42no—
310C4×C13—41no—
311C4×C13C2×#11711yescharacteristic
312C4×C13C4×#4111yescharacteristic
313C4×C13#53211yescharacteristic
314C4×C13#53211yescharacteristic
315Dic13—42no—
316Dic13—42no—
317Dic13—42no—
318Dic13—41no—
319C2×#41—131no—
320C2×#41C22×D1311yescharacteristic
321#135—262no—
322#135—262no—
323C2×Q16—131no—
324C2×SD16—131no—
325C2×SD16—131no—
326C2×D8—131no—
327C2×M16—131no—
328C2×M16—131no—
329C2×M16C22×D1311yescharacteristic
330C2×M16C22×D1311yescharacteristic
331C22×C8—131no—
332C22×C8—131no—
333C22×C8C22×D1311yescharacteristic
334C22×C8C22×D1311yescharacteristic
335C4×Q8—132no—
336C4×Q8C4×D1312yes—
337C4×D4—22no—
338C4×D4—132no—
339C4×D4—262no—
340C4×D4C4×D1312yes—
341#117—21no—
342#117—131no—
343#117—261no—
344#117C22×D1311yescharacteristic
345C2×C42—21no—
346C2×C42—131no—
347C2×C42—131no—
348C2×C42—261no—
349C2×C42C22×D1311yescharacteristic
350#108—262no—
351#108—262no—
352#107—132no—
353#106—132no—
354C4⋊C8—22no—
355C4⋊C8—22no—
356C4⋊C8—262no—
357C4⋊C8—262no—
358#104—262no—
359#104—262no—
360#104—262no—
361#104—262no—
362#103—132no—
363#103—132no—
364#102—132no—
365#102—132no—
366C22⋊C8—22no—
367C22⋊C8—22no—
368C22⋊C8—262no—
369C22⋊C8—262no—
370#97—21no—
371#97—132no—
372#97—132no—
373#97—262no—
374#97—262no—
375#97—261no—
376C4×C8—21no—
377C4×C8—262no—
378C4×C8—262no—
379C4×C8—261no—
380C4×C8C22⋊D1312yes—
381C4×C8C22⋊D1312yes—
382#95—262no—
383C2×C13—21no—
384C2×C13—21no—
385C2×C13—81no—
386C2×C13#229311yescharacteristic
387C2×C13#295512yes—
388D13—81no—
389#41—21no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—261no—
394#41—261no—
395#41—261no—
396#41—261no—
397C2×Q8—131no—
398C2×Q8C2×C4×D1311yescharacteristic
399C2×D4—21no—
400C2×D4—131no—
401C2×D4—261no—
402C2×D4C2×C4×D1311yescharacteristic
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—261no—
406C22×C4—261no—
407C22×C4—262no—
408C22×C4—261no—
409C22×C4#612712yes—
410C22×C4C23×D1311yescharacteristic
411Q16—262no—
412SD16—262no—
413SD16—262no—
414D8—262no—
415M16—21no—
416M16—21no—
417M16—21no—
418M16—21no—
419M16—261no—
420M16—261no—
421M16—261no—
422M16—261no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—131no—
430C2×C8—131no—
431C2×C8—132no—
432C2×C8—132no—
433C2×C8—132no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8C2×C22⋊D1312yes—
439C2×C8C2×C22⋊D1312yes—
440C4⋊C4—22no—
441C4⋊C4—132no—
442C4⋊C4—262no—
443C4⋊C4C2×C4×D1312yes—
444C22⋊C4—21no—
445C22⋊C4—22no—
446C22⋊C4—261no—
447C22⋊C4—262no—
448C42—22no—
449C42—21no—
450C42—132no—
451C42—132no—
452C42—262no—
453C42—261no—
454C42—261no—
455C42—261no—
456C42C2×C4×D1312yes—
457C42C2×C22⋊D1311yescharacteristic
458C42C2×C22⋊D1311yescharacteristic
459C13#2129611yescharacteristic, complemented, Sylow
460C23—21no—
461C23—261no—
462C23C2×#612711yescharacteristic
463Q8—21no—
464Q8—21no—
465Q8—261no—
466Q8—261no—
467D4—21no—
468D4—21no—
469D4—41no—
470D4—41no—
471D4—261no—
472D4—261no—
473D4—521no—
474D4—521no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—262no—
482C2×C4—262no—
483C2×C4—262no—
484C2×C4—261no—
485C2×C4—524no—
486C2×C4—522no—
487C2×C4—522no—
488C2×C4—521no—
489C2×C4—521no—
490C2×C4C4×C22⋊D1312yes—
491C2×C4C4×C22⋊D1312yes—
492C2×C4C22×C4×D1311yescharacteristic
493C2×C4#41×D1311yescharacteristic
494C2×C4#41×D1311yescharacteristic
495C2×C4#41×D1311yescharacteristic
496C2×C4#41×D1311yescharacteristic
497C2×C4C22×C22⋊D1311yescharacteristic
498C8—22no—
499C8—22no—
500C8—41no—
501C8—41no—
502C8—132no—
503C8—132no—
504C8—262no—
505C8—521no—
506C8—521no—
507C22—22no—
508C22—41no—
509C22—42no—
510C22—521no—
511C22—522no—
512C22#1171923311yescharacteristic
513C22#1171923311yescharacteristic
514C22C2×C4×C22⋊D1311yescharacteristic
515C4—22no—
516C4—22no—
517C4—41no—
518C4—42no—
519C4—522no—
520C4—522no—
521C4—521no—
522C4—522no—
523C4D13×#11711yescharacteristic
524C4#1171922711yescharacteristic
525C4#1171953711yescharacteristic
526C4#1171953711yescharacteristic
527C2—21no—
528C2—21no—
529C2—81no—
530C2—1041no—
531C2#1311729511yescharacteristic
532C2#1312373712yes—
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2922C2
socleC22×C13C2×C4×D4
prime radicalC2×#88204C22
cosocleC22×C4×C13C24
hypercenter#2922D13
hypocenterC13#21296
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #13123478C2semidirect
5. #13115586C2semidirect
6. #13115581C2semidirect
7. #13115550C2semidirect
8. #13115546C2semidirect
9. #13115543C2semidirect
10. #13115539C2semidirect
11. #13114743C2semidirect
12. #13114649C2semidirect
13. #13114646C2semidirect
14. #13114522C2semidirect
15. C13×#2922C2semidirect
42. #11718691C4semidirect
43. #11718687C4semidirect
44. #11718679C4semidirect
45. #11718675C4semidirect
196. #2922D13semidirect
459. C13#21296semidirect

Maximal subgroups

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

subgroupindex
#131236342
#131234782
#131157282
#131157232
#131155862
#131155812
#131155502
#131155462
#131155432
#131155392
#131147432
#131146492
#131146462
#131145222
C13×#29222
#2129613