Finite Group Databasebeta

← #15907744

Subgroups — #15907744

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119749C211yesmaximal, characteristic
2#13116272C212yesmaximal, complemented
3#13116025C212yesmaximal, complemented
4#13115631C211yesmaximal, characteristic, complemented
5#13115599C211yesmaximal, characteristic, complemented
6#13115158C212yesmaximal, complemented
7#13114963C211yesmaximal, characteristic, complemented
8#13114931C212yesmaximal, complemented
9#13114833C211yesmaximal, characteristic, complemented
10C4×#88049C211yesmaximal, characteristic, complemented
11C13×#2354C211yesmaximal, characteristic, complemented
12C2×C4×D4×C13C2211yescharacteristic
13C2×C13×#117C2212yes—
14C2×#88192—21no—
15C2×#88184C2212yes—
16C2×C4×D52C2211yescharacteristic
17C13×#390—21no—
18C13×#388—22no—
19C13×#384C2211yescharacteristic
20C13×#380C2212yes—
21C4×C13×C4⋊C4—21no—
22C4×C13×C4⋊C4C2211yescharacteristic
23#11718873C2212yes—
24C2×C22⋊#1055C2212yes—
25C2×C22⋊#1055C2212yes—
26#11718648—21no—
27C2×#88049C2211yescharacteristic
28C2×#88049C2211yescharacteristic
29C2×#88049C2212yes—
30C2×#88048C2212yes—
31#11718622—22no—
32#11718596C2211yescharacteristic
33C2×C4⋊#1055C2211yescharacteristic
34C2×C4×#1055C2211yescharacteristic
35#11718121C2212yes—
36#11718121C2212yes—
37#11718121C2211yescharacteristic
38#11718121C2211yescharacteristic
39#11718121C2212yes—
40#11718121C2212yes—
41C22×D4×C13D411yescharacteristic
42C23×C4×C13C2312yes—
43C22×C22⋊D13—22no—
44C22×D52C2311yescharacteristic
45C22×C4×D13—21no—
46C4×D4×C13—22no—
47C4×D4×C13—22no—
48C13×#117—24no—
49C13×#117—42no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C13×C4⋊C4C2311yescharacteristic
54C2×C13×C4⋊C4C2312yes—
55C2×C13×C4⋊C4C2311yescharacteristic
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4D412yes—
59C2×C42×C13—21no—
60C2×C42×C13—22no—
61C2×C42×C13C2311yescharacteristic
62C2×C22⋊Dic13—22no—
63#88192—44no—
64#88184—24no—
65#88184—42no—
66C2×#6103—21no—
67C2×#6103—22no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13C2311yescharacteristic
71C2×C4⋊Dic13C2312yes—
72C22×#1055C2311yescharacteristic
73C22×#1055C2311yescharacteristic
74C22×#1055C2312yes—
75C4×D52—22no—
76C4×D52—22no—
77C13×#95—22no—
78C13×#95—21no—
79#88071—22no—
80C22⋊#1055—42no—
81C22⋊#1055—42no—
82#88049—22no—
83#88049—22no—
84#88049—42no—
85#88048—42no—
86C4⋊#1055—22no—
87C4×#1055—22no—
88#24966—131nomaximal, Sylow
89C24×C13C2×D412yes—
90C23×D13—21no—
91C2×D4×C13—22no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C22×C4×C13—21no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—21no—
102C22×C4×C13—22no—
103C22×C4×C13C2×D412yes—
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2411yescharacteristic
107C2×C22⋊D13—44no—
108C2×C22⋊D13—44no—
109C2×C22⋊D13—82no—
110C22×Dic13—21no—
111C22×Dic13—22no—
112C2×D52—21no—
113C2×D52—21no—
114C2×D52—21no—
115C2×D52—21no—
116C2×D52—21no—
117C2×D52#4112yes—
118C2×C4×D13—42no—
119C2×C4×D13—42no—
120C2×C4×D13—42no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—42no—
128C13×C4⋊C4—81no—
129C13×C4⋊C4#4112yes—
130C13×C22⋊C4—24no—
131C13×C22⋊C4—44no—
132C13×C22⋊C4—82no—
133C42×C13—44no—
134C42×C13—42no—
135C42×C13#4112yes—
136C42×C13#4112yes—
137C22⋊Dic13—44no—
138#6103—44no—
139#6103—42no—
140C4⋊Dic13—21no—
141C4⋊Dic13—21no—
142C4⋊Dic13—22no—
143C4⋊Dic13—22no—
144C4⋊Dic13—42no—
145C4⋊Dic13—81no—
146C2×#1055—21no—
147C2×#1055—21no—
148C2×#1055—22no—
149C2×#1055—21no—
150C2×#1055—21no—
151C2×#1055—21no—
152C2×#1055—21no—
153C2×#1055—22no—
154C2×#1055—22no—
155#2537—131no—
156#2354D1311yescharacteristic, complemented
157#2077—132no—
158#2034—132no—
159#1954—131no—
160#1948—131no—
161#1875—132no—
162#1834—131no—
163#1825—132no—
164#1802—131no—
165C4×#102—131no—
166C23×C13—22no—
167C23×C13—22no—
168C23×C13—22no—
169C23×C13—22no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13C22×D411yescharacteristic
174C22×D13—22no—
175C22×D13—41no—
176C22×D13—41no—
177C22×D13—41no—
178C22×D13—41no—
179C22×D13—41no—
180C22×D13—41no—
181D4×C13—44no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—22no—
187C2×C4×C13—22no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—42no—
200C2×C4×C13#12312yes—
201C2×C4×C13#12312yes—
202C2×C4×C13#13512yes—
203C2×C4×C13AGL(1,ℤ/8)12yes—
204C2×C4×C13C2×#4111yescharacteristic
205C2×C4×C13C2×#4111yescharacteristic
206C2×C4×C13C2×#4111yescharacteristic
207C2×C4×C13C2×#4111yescharacteristic
208C2×C4×C13H(5,𝔽2)11yescharacteristic
209C2×C4×C13H(5,𝔽2)11yescharacteristic
210C22⋊D13—88no—
211C2×Dic13—41no—
212C2×Dic13—42no—
213C2×Dic13—41no—
214C2×Dic13—42no—
215C2×Dic13—41no—
216C2×Dic13—42no—
217D52—22no—
218D52—22no—
219D52—41no—
220D52—41no—
221C4×D13—84no—
222#1055—42no—
223#1055—41no—
224#1055—41no—
225C2×#121—132no—
226C2×#121—261no—
227C2×C4×D4—131no—
228C2×C4×D4C2×D1311yescharacteristic
229C2×#117C2×D1312yes—
230C2×#106—132no—
231C2×C4⋊C8—131no—
232C2×#102—131no—
233C2×#102—131no—
234C2×#102—132no—
235C2×C22⋊C8—132no—
236C2×C22⋊C8—132no—
237C2×C4×C8—131no—
238#394—262no—
239#390—21no—
240#388—22no—
241#384—131no—
242#384C2×D1311yescharacteristic
243#380—132no—
244#380—261no—
245#380C2×D1312yes—
246C4×C4⋊C4—21no—
247C4×C4⋊C4C2×D1311yescharacteristic
248#340—132no—
249#340—131no—
250#340—132no—
251#340—131no—
252#340—132no—
253#340—132no—
254C22×C13—42no—
255C22×C13—42no—
256C22×C13—42no—
257C22×C13—42no—
258C22×C13—42no—
259C22×C13—42no—
260C22×C13—42no—
261C22×C13C2×#12311yescharacteristic
262C22×C13#54611yescharacteristic
263C22×C13#54611yescharacteristic
264C22×C13C2×#13511yescharacteristic
265C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C13#57711yescharacteristic
267C22×C13#57711yescharacteristic
268C2×D13—42no—
269C2×D13—42no—
270C2×D13—42no—
271C2×D13—81no—
272C2×D13—81no—
273C2×D13—81no—
274C2×D13—81no—
275C4×C13—22no—
276C4×C13—42no—
277C4×C13—42no—
278C4×C13—82no—
279C4×C13—81no—
280C4×C13#48214yes—
281C4×C13#52911yescharacteristic
282C4×C13#54011yescharacteristic
283C4×C13#55311yescharacteristic
284C4×C13#55511yescharacteristic
285Dic13—81no—
286Dic13—82no—
287C22×D4—131no—
288C22×D4—262no—
289C22×D4C22⋊D1311yescharacteristic
290C23×C4—261no—
291C23×C4C22×D1312yes—
292C22×C8—131no—
293C22×C8—131no—
294C22×C8—132no—
295#121—264no—
296#121—522no—
297#121—524no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4—262no—
301C4×D4—262no—
302#117—24no—
303#117—42no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—131no—
307C2×C4⋊C4—132no—
308C2×C4⋊C4—261no—
309C2×C4⋊C4—261no—
310C2×C4⋊C4C22⋊D1311yescharacteristic
311C2×C4⋊C4C22×D1312yes—
312C2×C4⋊C4C22×D1311yescharacteristic
313C2×C4⋊C4C22×D1311yescharacteristic
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—262no—
317C2×C22⋊C4—261no—
318C2×C22⋊C4—262no—
319C2×C22⋊C4C22⋊D1312yes—
320C2×C42—22no—
321C2×C42—21no—
322C2×C42C22×D1311yescharacteristic
323#106—522no—
324C4⋊C8—262no—
325#102—262no—
326#102—262no—
327#102—522no—
328C22⋊C8—522no—
329C22⋊C8—522no—
330C4×C8—262no—
331#95—22no—
332#95—21no—
333#95—262no—
334C2×C13—82no—
335C2×C13#242011yescharacteristic
336C2×C13C2×#48211yescharacteristic
337C2×C13#309911yescharacteristic
338C2×C13#330311yescharacteristic
339C2×C13#330311yescharacteristic
340C2×C13#332411yescharacteristic
341C2×C13#333211yescharacteristic
342D13—82no—
343C24—261no—
344C24C2×C22⋊D1312yes—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—132no—
349C2×D4—261no—
350C2×D4—261no—
351C2×D4—261no—
352C2×D4—261no—
353C2×D4—261no—
354C2×D4—524no—
355C2×D4—524no—
356C2×D4—1042no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—261no—
367C22×C4—262no—
368C22×C4—522no—
369C22×C4—522no—
370C22×C4—522no—
371C22×C4C2×C22⋊D1312yes—
372C22×C4C2×C22⋊D1311yescharacteristic
373C22×C4C2×C22⋊D1311yescharacteristic
374C22×C4C23×D1311yescharacteristic
375C2×C8—261no—
376C2×C8—261no—
377C2×C8—262no—
378C2×C8—261no—
379C2×C8—261no—
380C2×C8—262no—
381C2×C8—261no—
382C2×C8—261no—
383C2×C8—262no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—42no—
391C4⋊C4—81no—
392C4⋊C4—261no—
393C4⋊C4—261no—
394C4⋊C4—262no—
395C4⋊C4—262no—
396C4⋊C4—522no—
397C4⋊C4—1041no—
398C4⋊C4#612912yes—
399C22⋊C4—24no—
400C22⋊C4—44no—
401C22⋊C4—82no—
402C22⋊C4—524no—
403C22⋊C4—524no—
404C22⋊C4—522no—
405C42—44no—
406C42—42no—
407C42#612712yes—
408C42#612712yes—
409C13#2496611yescharacteristic, complemented, Sylow
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—262no—
418C23—521no—
419C23—521no—
420C23—521no—
421C23—521no—
422C23—521no—
423C23—521no—
424C23C22×C22⋊D1311yescharacteristic
425D4—44no—
426D4—262no—
427D4—262no—
428D4—521no—
429D4—521no—
430D4—1048no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—521no—
450C2×C4—521no—
451C2×C4—522no—
452C2×C4—521no—
453C2×C4—522no—
454C2×C4—522no—
455C2×C4—1044no—
456C2×C4#8818312yes—
457C2×C4#8818312yes—
458C2×C4#8820312yes—
459C2×C4#8820412yes—
460C2×C4C2×#612711yescharacteristic
461C2×C4C2×#612711yescharacteristic
462C2×C4C2×#612911yescharacteristic
463C2×C4#8825111yescharacteristic
464C2×C4#41×D1311yescharacteristic
465C2×C4#8825611yescharacteristic
466C8—521no—
467C8—522no—
468C8—521no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—522no—
477C22—522no—
478C22—522no—
479C22—1041no—
480C22—1041no—
481C22—1041no—
482C22—1041no—
483C22C2×#8818311yescharacteristic
484C22#1171951111yescharacteristic
485C22C2×#8820311yescharacteristic
486C22C2×#8820411yescharacteristic
487C22#1171953411yescharacteristic
488C22#1171954111yescharacteristic
489C22#1171954211yescharacteristic
490C4—22no—
491C4—42no—
492C4—42no—
493C4—81no—
494C4—82no—
495C4—1041no—
496C4—1042no—
497C4#1171866414yes—
498C4#1171926211yescharacteristic
499C4#1171926311yescharacteristic
500C4#1171926711yescharacteristic
501C4#1171926811yescharacteristic
502C2—82no—
503C2—1042no—
504C2#1311832211yescharacteristic
505C2C2×#1171866411yescharacteristic
506C2#1312482511yescharacteristic
507C2#1312675811yescharacteristic
508C2#1312676411yescharacteristic
509C2#1312706111yescharacteristic
510C2#1312716311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2354C2
socleC23×C13C22×D4
prime radical#13119749C2
hypercenter#2354D13
hypocenterC13#24966
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13116272C2semidirect
3. #13116025C2semidirect
4. #13115631C2semidirect
5. #13115599C2semidirect
6. #13115158C2semidirect
7. #13114963C2semidirect
8. #13114931C2semidirect
9. #13114833C2semidirect
10. C4×#88049C2semidirect
11. C13×#2354C2semidirect
156. #2354D13semidirect
409. C13#24966semidirect

Maximal subgroups

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

subgroupindex
#131197492
#131162722
#131160252
#131156312
#131155992
#131151582
#131149632
#131149312
#131148332
C4×#880492
C13×#23542
#2496613