Finite Group Databasebeta

← #15867347

Subgroups — #15867347

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123634C211yesmaximal, characteristic
2#13123485C211yesmaximal, 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
12C4×#88065C211yesmaximal, characteristic, complemented
13C4×#88077C211yesmaximal, characteristic, complemented
14#97×Dic13C211yesmaximal, characteristic, complemented
15C13×#2923C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17C2×#88204C2211yescharacteristic
18C4×#6127C2211yescharacteristic
19C13×#433—22no—
20C13×#432—22no—
21C13×#424C2211yescharacteristic
22C13×#424C2211yescharacteristic
23C13×#408C2211yescharacteristic
24C13×#408C2211yescharacteristic
25C4×C13×M16C2211yescharacteristic
26C2×C13×#97C2211yescharacteristic
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
48C42×Dic13C2211yescharacteristic
49C4×#6099C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718370—22no—
52#11718366—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×Dic13—22no—
81C2×C4×Dic13C2311yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×#6099C2311yescharacteristic
84C2×#6099C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C4×D52C2×C412yes—
88#88126—21no—
89C42×D13—21no—
90C4×Dic26C2×C412yes—
91C13×C4⋊C8—22no—
92C13×C4⋊C8—22no—
93C13×C22⋊C8—22no—
94C13×C22⋊C8—22no—
95C13×#97—21no—
96C13×#97D412yes—
97C13×#97D412yes—
98C4×C8×C13—21no—
99#88077—22no—
100#88077—22no—
101#88075C2×C412yes—
102#88072C2×C412yes—
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#21297—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—21no—
132C22×C4×C13—22no—
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—21no—
144C2×C4×D13—22no—
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—44no—
180C4×Dic13#4112yes—
181C4×Dic13#4112yes—
182#6099—21no—
183#6099—21no—
184#6099—21no—
185#6099—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055C22×C412yes—
191C2×#1055C22×C411yescharacteristic
192C2×#1055C22×C411yescharacteristic
193C2×#1055#4112yes—
194C2×#1055#4112yes—
195#2943—131no—
196#2923—131no—
197#2923D1311yescharacteristic, complemented
198#1975—131no—
199#1974—131no—
200#1946—131no—
201#1945—131no—
202#1938—131no—
203#1938—131no—
204#1937—131no—
205#1937—131no—
206#1778—131no—
207C4×#104—131no—
208C4×#104—131no—
209C4×#97—131no—
210C23×C13—21no—
211C23×C13C2×#4111yescharacteristic
212C22×D13—21no—
213Q8×C13—21no—
214Q8×C13—21no—
215D4×C13—21no—
216D4×C13—21no—
217D4×C13—41no—
218D4×C13—41no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—42no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—82no—
225C2×C4×C13C4×D412yes—
226C2×C4×C13C4×D412yes—
227C2×C4×C13C23×C411yescharacteristic
228C2×C4×C13C22×D411yescharacteristic
229C2×C4×C13C2×#4111yescharacteristic
230C2×C4×C13C2×#4111yescharacteristic
231C2×C4×C13C2×#4111yescharacteristic
232C2×C4×C13C2×#4111yescharacteristic
233C22⋊D13—41no—
234C22⋊D13—41no—
235C2×Dic13—24no—
236C2×Dic13—22no—
237C2×Dic13—21no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—42no—
241D52—21no—
242D52—21no—
243C4×D13—41no—
244C4×D13—41no—
245C4×D13—82no—
246Dic26—21no—
247Dic26—21no—
248C8×C13—22no—
249C8×C13—22no—
250C8×C13—41no—
251C8×C13—41no—
252#1055—22no—
253#1055—41no—
254#1055—41no—
255#1055#11712yes—
256#1055#11712yes—
257C2×#135—131no—
258C4×#41—131no—
259C4×#41C2×D1311yescharacteristic
260#442—132no—
261#441—132no—
262#440—132no—
263#440—132no—
264#433—22no—
265#433—262no—
266#432—22no—
267#432—262no—
268C2×#108—131no—
269C2×#108—131no—
270#427—131no—
271#424—131no—
272#424—131no—
273#424C2×D1311yescharacteristic
274#424C2×D1311yescharacteristic
275C2×#104—131no—
276C2×#104—131no—
277C2×#104—131no—
278C2×#104—131no—
279#416—131no—
280#416—131no—
281#408—131no—
282#408—131no—
283#408C2×D1311yescharacteristic
284#408C2×D1311yescharacteristic
285C4×M16—131no—
286C4×M16C2×D1311yescharacteristic
287C2×#97—131no—
288C2×#97—131no—
289C2×#97—131no—
290C2×#97C2×D1311yescharacteristic
291C2×C4×C8—131no—
292C2×C4×C8—131no—
293C43—131no—
294#341—131no—
295#341—131no—
296#339—131no—
297#339—131no—
298#339—131no—
299#339—131no—
300C22×C13—22no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13C2×C4×D411yescharacteristic
304C22×C13#52911yescharacteristic
305C22×C13#52911yescharacteristic
306C2×D13—42no—
307C2×D13—41no—
308C4×C13—22no—
309C4×C13—22no—
310C4×C13—42no—
311C4×C13—41no—
312C4×C13C2×#11711yescharacteristic
313C4×C13C4×#4111yescharacteristic
314C4×C13#53211yescharacteristic
315C4×C13#53211yescharacteristic
316Dic13—24no—
317Dic13—42no—
318Dic13—42no—
319Dic13—41no—
320C2×#41—131no—
321C2×#41C22×D1311yescharacteristic
322#135—262no—
323#135—262no—
324C2×Q16—131no—
325C2×SD16—131no—
326C2×SD16—131no—
327C2×D8—131no—
328C2×M16—131no—
329C2×M16—131no—
330C2×M16C22×D1311yescharacteristic
331C2×M16C22×D1311yescharacteristic
332C22×C8—131no—
333C22×C8—131no—
334C22×C8C22×D1311yescharacteristic
335C22×C8C22×D1311yescharacteristic
336C4×Q8—132no—
337C4×Q8C4×D1312yes—
338C4×D4—22no—
339C4×D4—132no—
340C4×D4—262no—
341C4×D4C4×D1312yes—
342#117—21no—
343#117—131no—
344#117—261no—
345#117C22×D1311yescharacteristic
346C2×C42—21no—
347C2×C42—131no—
348C2×C42—131no—
349C2×C42—261no—
350C2×C42—262no—
351C2×C42C22×D1311yescharacteristic
352#108—262no—
353#108—262no—
354#107—132no—
355#106—132no—
356C4⋊C8—22no—
357C4⋊C8—22no—
358C4⋊C8—262no—
359C4⋊C8—262no—
360#104—262no—
361#104—262no—
362#104—262no—
363#104—262no—
364#103—132no—
365#103—132no—
366#102—132no—
367#102—132no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—262no—
371C22⋊C8—262no—
372#97—21no—
373#97—132no—
374#97—132no—
375#97—262no—
376#97—262no—
377#97—261no—
378#97C22⋊D1312yes—
379#97C22⋊D1312yes—
380C4×C8—21no—
381C4×C8—262no—
382C4×C8—262no—
383C4×C8—261no—
384C2×C13—21no—
385C2×C13—21no—
386C2×C13—81no—
387C2×C13#229311yescharacteristic
388C2×C13#295612yes—
389D13—81no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—261no—
395#41—261no—
396#41—261no—
397#41—261no—
398C2×Q8—131no—
399C2×Q8C2×C4×D1311yescharacteristic
400C2×D4—21no—
401C2×D4—131no—
402C2×D4—261no—
403C2×D4C2×C4×D1311yescharacteristic
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—261no—
407C22×C4—261no—
408C22×C4—261no—
409C22×C4—262no—
410C22×C4#612712yes—
411C22×C4C23×D1311yescharacteristic
412Q16—262no—
413SD16—262no—
414SD16—262no—
415D8—262no—
416M16—21no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—261no—
421M16—261no—
422M16—261no—
423M16—261no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—131no—
431C2×C8—131no—
432C2×C8—132no—
433C2×C8—132no—
434C2×C8—132no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8C2×C22⋊D1312yes—
440C2×C8C2×C22⋊D1312yes—
441C4⋊C4—22no—
442C4⋊C4—132no—
443C4⋊C4—262no—
444C4⋊C4C2×C4×D1312yes—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—261no—
448C22⋊C4—262no—
449C42—22no—
450C42—21no—
451C42—132no—
452C42—132no—
453C42—262no—
454C42—261no—
455C42—261no—
456C42—261no—
457C42—524no—
458C42C2×C4×D1312yes—
459C42C2×C22⋊D1311yescharacteristic
460C42C2×C22⋊D1311yescharacteristic
461C13#2129711yescharacteristic, complemented, Sylow
462C23—21no—
463C23—261no—
464C23C2×#612711yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—261no—
468Q8—261no—
469D4—21no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—261no—
474D4—261no—
475D4—521no—
476D4—521no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—82no—
483C2×C4—264no—
484C2×C4—262no—
485C2×C4—262no—
486C2×C4—262no—
487C2×C4—261no—
488C2×C4—522no—
489C2×C4—521no—
490C2×C4—521no—
491C2×C4—1042no—
492C2×C4C4×C22⋊D1312yes—
493C2×C4C4×C22⋊D1312yes—
494C2×C4C22×C4×D1311yescharacteristic
495C2×C4#41×D1311yescharacteristic
496C2×C4#41×D1311yescharacteristic
497C2×C4#41×D1311yescharacteristic
498C2×C4#41×D1311yescharacteristic
499C2×C4C22×C22⋊D1311yescharacteristic
500C8—22no—
501C8—22no—
502C8—41no—
503C8—41no—
504C8—132no—
505C8—132no—
506C8—262no—
507C8—521no—
508C8—521no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—521no—
513C22—522no—
514C22#1171923311yescharacteristic
515C22#1171923311yescharacteristic
516C22C2×C4×C22⋊D1311yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—42no—
521C4—264no—
522C4—522no—
523C4—521no—
524C4—522no—
525C4D13×#11711yescharacteristic
526C4#1171922711yescharacteristic
527C4#1171953711yescharacteristic
528C4#1171953711yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—1041no—
533C2#1311729511yescharacteristic
534C2#1312374312yes—
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2923C2
socleC22×C13C2×C4×D4
prime radicalC2×#88204C22
cosocleC22×C4×C13C24
hypercenter#2923D13
hypocenterC13#21297
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #13123485C2semidirect
5. #13115586C2semidirect
6. #13115581C2semidirect
7. #13115550C2semidirect
8. #13115546C2semidirect
9. #13115543C2semidirect
10. #13115539C2semidirect
11. #13114743C2semidirect
12. C4×#88065C2semidirect
13. C4×#88077C2semidirect
14. #97×Dic13C2semidirect
15. C13×#2923C2semidirect
42. #11718691C4semidirect
43. #11718687C4semidirect
44. #11718679C4semidirect
45. #11718675C4semidirect
197. #2923D13semidirect
461. C13#21297semidirect

Maximal subgroups

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

subgroupindex
#131236342
#131234852
#131157282
#131157232
#131155862
#131155812
#131155502
#131155462
#131155432
#131155392
#131147432
C4×#880652
C4×#880772
#97×Dic132
C13×#29232
#2129713