Finite Group Databasebeta

← #16019403

Subgroups — #16019403

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718856C211yesmaximal, characteristic, complemented
2C22×#88067C211yesmaximal, characteristic, complemented
3D4×Dic52C211yesmaximal, characteristic, complemented
4#13117108C211yesmaximal, characteristic, complemented
5#13116947C211yesmaximal, characteristic, complemented
6#13116925C211yesmaximal, characteristic, complemented
7#13116895C211yesmaximal, characteristic, complemented
8#13116881C211yesmaximal, characteristic, complemented
9#13116776C211yesmaximal, characteristic, complemented
10#13116769C211yesmaximal, characteristic, complemented
11#13116765C211yesmaximal, characteristic, complemented
12#13116752C211yesmaximal, characteristic, complemented
13#13116700C211yesmaximal, characteristic, complemented
14#13116662C211yesmaximal, characteristic, complemented
15C13×#3280C211yesmaximal, characteristic
16C2×C13×#135C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C13×#546—21no—
19C22×Dic52C2211yescharacteristic
20C22×Dic52C2211yescharacteristic, complemented
21D4×Dic26—21no—
22C13×#495C2211yescharacteristic
23C13×#467C2211yescharacteristic
24C13×#466C2211yescharacteristic
25C13×#463—21no—
26C13×#450—21no—
27C13×#449—21no—
28C4×C13×D8C2211yescharacteristic
29C8×D4×C13C2211yescharacteristic
30#11718856—24no—
31C2×#88069C2211yescharacteristic, complemented
32C2×#88069C2211yescharacteristic, complemented
33C2×#88069C2211yescharacteristic, complemented
34C2×#88067—24no—
35C2×#88067C2211yescharacteristic
36C2×#88067C2211yescharacteristic
37C2×#88067C2211yescharacteristic
38C2×#88067C2211yescharacteristic
39C2×#88067C2211yescharacteristic
40C2×#88067C2211yescharacteristic
41#11718777C2211yescharacteristic
42#11718777C2211yescharacteristic, complemented
43C2×#88052C2211yescharacteristic, complemented
44C22×#6090C2211yescharacteristic
45#11718510—21no—
46#11718400—21no—
47#11718400—21no—
48#11718360C2211yescharacteristic, complemented
49C4×Dic52C2211yescharacteristic, complemented
50#11718156C2211yescharacteristic, complemented
51#11718154C2211yescharacteristic
52#11718154C2211yescharacteristic
53C22⋊#6090C2211yescharacteristic
54C22⋊#6090C2211yescharacteristic, complemented
55#11718084C2211yescharacteristic, complemented
56#11718084C2211yescharacteristic, complemented
57#11718084C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59C4⋊#6090C2211yescharacteristic, complemented
60#11718053C2211yescharacteristic, complemented
61C2×C13×#41—21no—
62C22×D4×C13—21no—
63C22×Dic26—21no—
64C22×Dic26—21no—
65C13×#135—22no—
66C13×#135—41no—
67C2×C13×Q16C2311yescharacteristic
68C2×C13×SD16—21no—
69C2×C13×SD16—21no—
70C2×C13×D8—22no—
71C2×C13×D8—21no—
72C2×C13×D8—41no—
73C2×C13×D8C2311yescharacteristic
74C2×C13×D8C2311yescharacteristic
75C22×C8×C13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C13×#124—21no—
78C13×#123—41no—
79C13×C22⋊Q8—21no—
80C13×#121—21no—
81C13×#121—41no—
82C13×#120—41no—
83C4×D4×C13—21no—
84C4×D4×C13D411yescharacteristic
85C2×C13×C22⋊C4—41no—
86D4×Dic13—41no—
87#88178—21no—
88#88178—21no—
89C2×Dic52—22no—
90C2×Dic52—22no—
91C2×Dic52—21no—
92C2×Dic52—21no—
93C2×Dic52—21no—
94C2×Dic52—41no—
95C2×Dic52—41no—
96C2×Dic52C2311yescharacteristic
97C2×Dic52C2311yescharacteristic
98C2×Dic52C2311yescharacteristic
99#88142—41no—
100#88132—41no—
101#88132—41no—
102#88123—21no—
103C4×Dic26—21no—
104C13×#107C2311yescharacteristic
105C13×C4⋊C8D411yescharacteristic
106C13×#103—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×C22⋊C8D411yescharacteristic
110C13×C22⋊C8D411yescharacteristic
111C4×C8×C13C2311yescharacteristic
112#88069—22no—
113#88069—22no—
114#88069—41no—
115#88067—22no—
116#88067—22no—
117#88067—22no—
118#88067—22no—
119#88067—41no—
120#88067D414yescomplemented
121#88058C2311yescharacteristic
122#88056—21no—
123#88056—21no—
124#88056—21no—
125#88052—22no—
126C2×#6090—22no—
127C2×#6090C2311yescharacteristic
128C2×#6090C2311yescharacteristic
129C2×#6090C2311yescharacteristic
130C2×#6090C2311yescharacteristic
131#33832—131nomaximal, Sylow
132C24×C13—41no—
133C13×#41—42no—
134C13×#41—81no—
135C2×Q8×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—42no—
139C2×D4×C13—41no—
140C2×D4×C13—41no—
141C2×D4×C13—41no—
142C2×D4×C13—81no—
143C2×D4×C13D811yescharacteristic
144C22×C4×C13—41no—
145C22×C4×C13—41no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×Dic13—41no—
149C22×Dic13—41no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—42no—
154C2×Dic26—42no—
155C2×Dic26—41no—
156C2×Dic26—41no—
157C2×Dic26—81no—
158C2×Dic26—81no—
159C13×Q16—21no—
160C13×Q16—21no—
161C13×SD16—42no—
162C13×SD16—81no—
163C13×D8—21no—
164C13×D8—21no—
165C13×D8—21no—
166C13×D8—42no—
167C13×D8C2×D412yes—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2411yescharacteristic
176C13×C4⋊C4—21no—
177C13×C4⋊C4—41no—
178C13×C4⋊C4D811yescharacteristic
179C13×C22⋊C4—41no—
180C13×C22⋊C4—41no—
181C13×C22⋊C4—41no—
182C13×C22⋊C4—41no—
183C13×C22⋊C4—41no—
184C13×C22⋊C4D811yescharacteristic
185C13×C22⋊C4D811yescharacteristic
186C42×C13C2×D411yescharacteristic
187C22⋊Dic13—41no—
188C22⋊Dic13—41no—
189C4⋊Dic13—21no—
190C4⋊Dic13—41no—
191C4⋊Dic13—41no—
192#6101—41no—
193#6101—41no—
194#6101—41no—
195C4×Dic13—41no—
196Dic52—21no—
197Dic52—21no—
198Dic52—21no—
199Dic52—21no—
200Dic52—21no—
201Dic52—42no—
202Dic52—42no—
203Dic52—81no—
204Dic52C2×D412yes—
205#6090—21no—
206#6090—21no—
207#6090—21no—
208#6090C2×D412yes—
209C2×#510—131no—
210C22×SD32—131no—
211D4×Q16—131no—
212#3280D1311yescharacteristic
213#2251—131no—
214#2220—131no—
215#2216—131no—
216#2211—131no—
217#2208—131no—
218#2189—131no—
219#2188—131no—
220#2187—131no—
221#2185—131no—
222#2175—131no—
223#2168—131no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—82no—
227C23×C13—82no—
228C23×C13—161no—
229C23×C13C2×D811yescharacteristic
230C23×C13C2×D811yescharacteristic
231Q8×C13—41no—
232Q8×C13—41no—
233D4×C13—22no—
234D4×C13—22no—
235D4×C13—41no—
236D4×C13—41no—
237D4×C13—41no—
238D4×C13—82no—
239D4×C13—82no—
240D4×C13—161no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—82no—
248C2×C4×C13—161no—
249C2×C4×C13C2×D811yescharacteristic
250C2×C4×C13C2×D811yescharacteristic
251C2×C4×C13C2×D811yescharacteristic
252C2×C4×C13C2×D811yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—82no—
259C2×Dic13—82no—
260Dic26—22no—
261Dic26—41no—
262Dic26—41no—
263Dic26—41no—
264Dic26—41no—
265Dic26—41no—
266Dic26—82no—
267Dic26—82no—
268C8×C13—21no—
269C8×C13—21no—
270C8×C13—21no—
271C8×C13C22×D411yescharacteristic
272C8×C13H(5,𝔽2)11yescharacteristic
273C2×#135C2×D1311yescharacteristic
274C22×Q16—131no—
275C22×Q16—131no—
276C22×D8C2×D1311yescharacteristic
277D4×Q8—261no—
278#546—21no—
279#510—264no—
280C2×Q32—131no—
281C2×Q32—131no—
282C2×Q32—131no—
283C2×SD32—131no—
284C2×SD32—131no—
285C2×SD32—131no—
286C2×SD32—131no—
287C2×SD32—131no—
288C2×SD32—131no—
289C2×SD32—264no—
290C2×M32—131no—
291C22×C16—131no—
292#495C2×D1311yescharacteristic
293#494—131no—
294#467—131no—
295#467—131no—
296#467C2×D1311yescharacteristic
297#466C2×D1311yescharacteristic
298#463—21no—
299#462—261no—
300#451—261no—
301#451—261no—
302#450—21no—
303#449—21no—
304C4×Q16—131no—
305C4×D8C2×D1311yescharacteristic
306C8×D4C2×D1311yescharacteristic
307#366—131no—
308C4⋊C16—131no—
309#358—131no—
310#358—131no—
311#358—131no—
312#358—131no—
313#357—131no—
314#357—131no—
315C22⋊C16—131no—
316C22⋊C16—131no—
317#346—131no—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13—42no—
324C22×C13—81no—
325C22×C13—81no—
326C22×C13—81no—
327C22×C13—81no—
328C22×C13—81no—
329C22×C13—164no—
330C22×C13#51012yescomplemented
331C22×C13C22×D811yescharacteristic
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13D4211yescharacteristic
339C4×C13#57611yescharacteristic
340Dic13—42no—
341Dic13—81no—
342Dic13—81no—
343Dic13—81no—
344C2×#41—21no—
345C22×Q8—261no—
346C22×Q8—261no—
347C22×D4—21no—
348#135—22no—
349#135—41no—
350C2×Q16—131no—
351C2×Q16—131no—
352C2×Q16—131no—
353C2×Q16—262no—
354C2×Q16—262no—
355C2×Q16—261no—
356C2×Q16—261no—
357C2×Q16—261no—
358C2×Q16—521no—
359C2×Q16—521no—
360C2×Q16C22×D1311yescharacteristic
361C2×SD16—21no—
362C2×SD16—21no—
363C2×D8—22no—
364C2×D8—21no—
365C2×D8—41no—
366C2×D8C22×D1311yescharacteristic
367C2×D8C22×D1311yescharacteristic
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
370C4⋊Q8—261no—
371C4⋊Q8—521no—
372#124—21no—
373#123—41no—
374C22⋊Q8—21no—
375C22⋊Q8—261no—
376C22⋊Q8—261no—
377C22⋊Q8—521no—
378C22⋊Q8—521no—
379#121—21no—
380#121—41no—
381#120—41no—
382C4×Q8—261no—
383C4×D4—21no—
384C4×D4—521no—
385C4×D4C22⋊D1311yescharacteristic
386C2×C22⋊C4—41no—
387Q32—262no—
388Q32—262no—
389Q32—521no—
390SD32—134no—
391SD32—262no—
392SD32—262no—
393SD32—262no—
394SD32—262no—
395SD32—521no—
396M32—262no—
397C2×C16—131no—
398C2×C16—131no—
399C2×C16—131no—
400C2×C16—131no—
401C2×C16—262no—
402#107—131no—
403#107C22×D1311yescharacteristic
404C4⋊C8C22⋊D1311yescharacteristic
405#103—21no—
406#103—261no—
407#103—261no—
408#103—261no—
409#102—21no—
410#102—21no—
411C22⋊C8C22⋊D1311yescharacteristic
412C22⋊C8C22⋊D1311yescharacteristic
413C4×C8C22×D1311yescharacteristic
414C2×C13—22no—
415C2×C13—41no—
416C2×C13—82no—
417C2×C13—161no—
418C2×C13D4×D811yescharacteristic
419C2×C13C2×#51011yescharacteristic
420C2×C13#341611yescharacteristic
421C24—41no—
422#41—42no—
423#41—81no—
424C2×Q8—21no—
425C2×Q8—261no—
426C2×Q8—261no—
427C2×Q8—261no—
428C2×Q8—522no—
429C2×Q8—522no—
430C2×Q8—521no—
431C2×Q8—521no—
432C2×Q8—1041no—
433C2×Q8—1041no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—81no—
441C2×D4#610411yescharacteristic
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—521no—
445C22×C4—521no—
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448Q16—21no—
449Q16—21no—
450Q16—132no—
451Q16—261no—
452Q16—261no—
453Q16—261no—
454Q16—261no—
455Q16—261no—
456Q16—522no—
457Q16—522no—
458Q16—1041no—
459SD16—42no—
460SD16—81no—
461D8—21no—
462D8—21no—
463D8—21no—
464D8—42no—
465D8D4×D1312yes—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×C22⋊D1311yescharacteristic
471C2×C8C2×C22⋊D1311yescharacteristic
472C2×C8C2×C22⋊D1311yescharacteristic
473C2×C8C23×D1311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—261no—
477C4⋊C4—521no—
478C4⋊C4—521no—
479C4⋊C4—521no—
480C4⋊C4—521no—
481C4⋊C4—521no—
482C4⋊C4#610411yescharacteristic
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—521no—
489C22⋊C4—521no—
490C22⋊C4#610411yescharacteristic
491C22⋊C4#610411yescharacteristic
492C42—521no—
493C42C2×C22⋊D1311yescharacteristic
494C16—132no—
495C16—261no—
496C16—261no—
497C16—261no—
498C13#3383211yescharacteristic, complemented, Sylow
499C23—41no—
500C23—41no—
501C23—82no—
502C23—82no—
503C23—161no—
504C23C2×#610411yescharacteristic
505C23C2×#610411yescharacteristic
506Q8—41no—
507Q8—41no—
508Q8—262no—
509Q8—521no—
510Q8—521no—
511Q8—521no—
512Q8—521no—
513Q8—521no—
514Q8—1042no—
515Q8—1042no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—82no—
522D4—82no—
523D4—161no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4—161no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—1042no—
537C2×C4—1042no—
538C2×C4C2×#610411yescharacteristic
539C2×C4C2×#610411yescharacteristic
540C2×C4C2×#610411yescharacteristic
541C2×C4C2×#610411yescharacteristic
542C2×C4C22×C22⋊D1311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8C2×D4×D1311yescharacteristic
547C8#8825111yescharacteristic
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—164no—
560C22#1171885612yescomplemented
561C22C22×#610411yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—81no—
567C4—81no—
568C4—522no—
569C4—1041no—
570C4—1041no—
571C4—1041no—
572C4D4×C22⋊D1311yescharacteristic
573C4#1171954011yescharacteristic
574C2—22no—
575C2—41no—
576C2—82no—
577C2—161no—
578C2D4×#610411yescharacteristic
579C2C2×#1171885611yescharacteristic
580C2#1312798311yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC13×#3280C2
socleC22×C13C22×D8
hypercenter#3280D13
hypocenterC13#33832
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. C2×#11718856C2semidirect
2. C22×#88067C2semidirect
3. D4×Dic52C2semidirect
4. #13117108C2semidirect
5. #13116947C2semidirect
6. #13116925C2semidirect
7. #13116895C2semidirect
8. #13116881C2semidirect
9. #13116776C2semidirect
10. #13116769C2semidirect
11. #13116765C2semidirect
12. #13116752C2semidirect
13. #13116700C2semidirect
14. #13116662C2semidirect
20. C22×Dic52C22semidirect
31. C2×#88069C22semidirect
32. C2×#88069C22semidirect
33. C2×#88069C22semidirect
42. #11718777C22semidirect
43. C2×#88052C22semidirect
48. #11718360C22semidirect
49. C4×Dic52C22semidirect
50. #11718156C22semidirect
54. C22⋊#6090C22semidirect
55. #11718084C22semidirect
56. #11718084C22semidirect
57. #11718084C22semidirect
58. #11718081C22semidirect
59. C4⋊#6090C22semidirect
60. #11718053C22semidirect
120. #88067D4semidirect
330. C22×C13#510semidirect
498. C13#33832semidirect
560. C22#11718856semidirect

Maximal subgroups

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

subgroupindex
C2×#117188562
C22×#880672
D4×Dic522
#131171082
#131169472
#131169252
#131168952
#131168812
#131167762
#131167692
#131167652
#131167522
#131167002
#131166622
C13×#32802
#3383213