Finite Group Databasebeta

← #15907746

Subgroups — #15907746

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#13117785C211yesmaximal, characteristic, complemented
2#13116273C212yesmaximal, complemented
3#13116022C212yesmaximal, complemented
4#13115631C211yesmaximal, characteristic, complemented
5#13115597C211yesmaximal, characteristic, complemented
6#13115159C212yesmaximal, complemented
7#13114963C211yesmaximal, characteristic, complemented
8#13114928C212yesmaximal, complemented
9#13114836C211yesmaximal, characteristic, complemented
10C4×#88072C211yesmaximal, characteristic, complemented
11C13×#2537C211yesmaximal, characteristic
12C2×C13×#121—21no—
13C2×C13×#121C2212yes—
14C2×C4×D4×C13C2211yescharacteristic
15C2×C4×D4×C13C2211yescharacteristic
16C2×#88180C2212yes—
17C13×#394—22no—
18C13×#384C2211yescharacteristic
19C13×#380—21no—
20C13×#380C2212yes—
21#11718882—21no—
22C2×#88072C2211yescharacteristic
23C2×#88072C2211yescharacteristic
24C2×#88072C2212yes—
25#11718873C2212yes—
26C2×C22⋊#1055C2212yes—
27C2×C22⋊#1055C2212yes—
28C4⋊C4×Dic13—21no—
29C2×#88048C2212yes—
30#11718612—22no—
31#11718596C2211yescharacteristic
32C4×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊#1055C2211yescharacteristic
34C2×C4×#1055C2211yescharacteristic
35#11718121C2212yes—
36#11718121C2212yes—
37#11718121C2211yescharacteristic
38#11718121C2211yescharacteristic
39#11718121C2212yes—
40#11718121C2212yes—
41C22×D4×C13—22no—
42C22×D4×C13D411yescharacteristic
43C22×D4×C13C2311yescharacteristic
44C23×C4×C13—21no—
45C23×C4×C13C2312yes—
46C13×#121—24no—
47C13×#121—42no—
48C13×#121—44no—
49C4×D4×C13—22no—
50C4×D4×C13—22no—
51C4×D4×C13—22no—
52C4×D4×C13—22no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C4⋊C4C2311yescharacteristic
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4D412yes—
62C2×C42×C13C2311yescharacteristic
63C2×C22⋊Dic13—22no—
64C2×C22⋊Dic13—22no—
65#88180—24no—
66#88180—42no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13C2312yes—
70C2×C4⋊Dic13C2311yescharacteristic
71C2×C4⋊Dic13C2311yescharacteristic
72C2×C4×Dic13—22no—
73C2×C4×Dic13—21no—
74C22×#1055C2311yescharacteristic
75C22×#1055C2311yescharacteristic
76C22×#1055C2312yes—
77C13×#95—22no—
78#88072—22no—
79#88072—22no—
80#88072—42no—
81#88071—21no—
82#88071—22no—
83C22⋊#1055—42no—
84C22⋊#1055—42no—
85#88048—42no—
86C4⋊#1055—22no—
87C4×#1055—22no—
88#24966—131nomaximal, Sylow
89C24×C13—21no—
90C24×C13C2×D412yes—
91C2×D4×C13—22no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—21no—
98C2×D4×C13—21no—
99C2×D4×C13—44no—
100C2×D4×C13—44no—
101C2×D4×C13—82no—
102C2×D4×C13#4112yes—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—42no—
112C22×C4×C13—42no—
113C22×C4×C13—42no—
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2411yescharacteristic
118C22×Dic13—21no—
119C22×Dic13—21no—
120C22×Dic13—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—42no—
127C13×C4⋊C4—81no—
128C13×C22⋊C4—24no—
129C13×C22⋊C4—44no—
130C13×C22⋊C4—44no—
131C13×C22⋊C4—42no—
132C42×C13#4112yes—
133C42×C13#4112yes—
134C22⋊Dic13—44no—
135C22⋊Dic13—82no—
136C4⋊Dic13—21no—
137C4⋊Dic13—21no—
138C4⋊Dic13—22no—
139C4⋊Dic13—22no—
140C4⋊Dic13—21no—
141C4⋊Dic13—42no—
142C4⋊Dic13—81no—
143C4⋊Dic13#4112yes—
144C4×Dic13—44no—
145C4×Dic13—42no—
146C2×#1055—21no—
147C2×#1055—21no—
148C2×#1055—21no—
149C2×#1055—21no—
150C2×#1055—22no—
151C2×#1055—21no—
152C2×#1055—21no—
153C2×#1055—22no—
154C2×#1055—22no—
155#2537D1311yescharacteristic
156#2354—131no—
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×C13—22no—
174C23×C13—41no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13C22×D411yescharacteristic
181D4×C13—22no—
182D4×C13—22no—
183D4×C13—41no—
184D4×C13—41no—
185D4×C13—44no—
186D4×C13—88no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—41no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—84no—
203C2×C4×C13#12312yes—
204C2×C4×C13#12312yes—
205C2×C4×C13#13512yes—
206C2×C4×C13AGL(1,ℤ/8)12yes—
207C2×C4×C13C2×#4111yescharacteristic
208C2×C4×C13C2×#4111yescharacteristic
209C2×C4×C13C2×#4111yescharacteristic
210C2×C4×C13C2×#4111yescharacteristic
211C2×C4×C13H(5,𝔽2)11yescharacteristic
212C2×C4×C13H(5,𝔽2)11yescharacteristic
213C2×Dic13—22no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13—42no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—42no—
220C2×Dic13—42no—
221C2×Dic13—41no—
222#1055—42no—
223#1055—41no—
224#1055—41no—
225C2×#121—21no—
226C2×#121C2×D1312yes—
227C2×C4×D4C2×D1311yescharacteristic
228C2×C4×D4C2×D1311yescharacteristic
229C2×#117—132no—
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—22no—
239#390—261no—
240#388—262no—
241#384—131no—
242#384C2×D1311yescharacteristic
243#380—21no—
244#380—132no—
245#380C2×D1312yes—
246C4×C4⋊C4—131no—
247C4×C4⋊C4—261no—
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×C13—42no—
262C22×C13—42no—
263C22×C13—42no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13C2×#12311yescharacteristic
269C22×C13#54611yescharacteristic
270C22×C13#54611yescharacteristic
271C22×C13C2×#13511yescharacteristic
272C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C13#57711yescharacteristic
274C22×C13#57711yescharacteristic
275C4×C13—22no—
276C4×C13—42no—
277C4×C13—81no—
278C4×C13—82no—
279C4×C13#48214yes—
280C4×C13#52911yescharacteristic
281C4×C13#54011yescharacteristic
282C4×C13#55311yescharacteristic
283C4×C13#55511yescharacteristic
284Dic13—42no—
285Dic13—82no—
286Dic13—81no—
287C22×D4—22no—
288C22×D4C22⋊D1311yescharacteristic
289C22×D4C22×D1311yescharacteristic
290C23×C4—21no—
291C23×C4C22×D1312yes—
292C22×C8—131no—
293C22×C8—131no—
294C22×C8—132no—
295#121—24no—
296#121—42no—
297#121—44no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302#117—264no—
303#117—522no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—131no—
307C2×C4⋊C4—132no—
308C2×C4⋊C4—131no—
309C2×C4⋊C4—261no—
310C2×C4⋊C4—261no—
311C2×C4⋊C4C22⋊D1311yescharacteristic
312C2×C4⋊C4C22×D1311yescharacteristic
313C2×C4⋊C4C22×D1312yes—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—262no—
318C2×C22⋊C4—262no—
319C2×C22⋊C4C22⋊D1312yes—
320C2×C42—262no—
321C2×C42—261no—
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—261no—
333#95—262no—
334C2×C13—82no—
335C2×C13—82no—
336C2×C13#242011yescharacteristic
337C2×C13C2×#48211yescharacteristic
338C2×C13#309911yescharacteristic
339C2×C13#330311yescharacteristic
340C2×C13#330311yescharacteristic
341C2×C13#332411yescharacteristic
342C2×C13#333211yescharacteristic
343C24—21no—
344C24C2×C22⋊D1312yes—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—44no—
354C2×D4—44no—
355C2×D4—82no—
356C2×D4#612912yes—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—261no—
369C22×C4—261no—
370C22×C4—262no—
371C22×C4C2×C22⋊D1312yes—
372C22×C4C2×C22⋊D1311yescharacteristic
373C22×C4C2×C22⋊D1311yescharacteristic
374C22×C4C23×D1311yescharacteristic
375C2×C8—261no—
376C2×C8—261no—
377C2×C8—261no—
378C2×C8—262no—
379C2×C8—261no—
380C2×C8—262no—
381C2×C8—261no—
382C2×C8—261no—
383C2×C8—262no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4—81no—
391C4⋊C4—132no—
392C4⋊C4—261no—
393C4⋊C4—261no—
394C4⋊C4—261no—
395C4⋊C4—262no—
396C4⋊C4—262no—
397C4⋊C4—522no—
398C4⋊C4—1041no—
399C22⋊C4—24no—
400C22⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—42no—
403C22⋊C4—524no—
404C22⋊C4—1042no—
405C42—524no—
406C42—522no—
407C42#612912yes—
408C42#612912yes—
409C13#2496611yescharacteristic, complemented, Sylow
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23C22×C22⋊D1311yescharacteristic
425D4—22no—
426D4—22no—
427D4—44no—
428D4—41no—
429D4—41no—
430D4—88no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—84no—
447C2×C4—262no—
448C2×C4—521no—
449C2×C4—521no—
450C2×C4—522no—
451C2×C4—521no—
452C2×C4—521no—
453C2×C4—522no—
454C2×C4—521no—
455C2×C4—522no—
456C2×C4#8818612yes—
457C2×C4#8818912yes—
458C2×C4#8818912yes—
459C2×C4#8820412yes—
460C2×C4C2×#612911yescharacteristic
461C2×C4C2×#612911yescharacteristic
462C2×C4C2×#612911yescharacteristic
463C2×C4#8825111yescharacteristic
464C2×C4#41×D1311yescharacteristic
465C2×C4#8825611yescharacteristic
466C8—521no—
467C8—521no—
468C8—522no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C2×#8818611yescharacteristic
484C22C2×#8818911yescharacteristic
485C22#1171951111yescharacteristic
486C22C2×#8820411yescharacteristic
487C22#1171953411yescharacteristic
488C22#1171954111yescharacteristic
489C22#1171954211yescharacteristic
490C4—22no—
491C4—42no—
492C4—81no—
493C4—82no—
494C4—522no—
495C4—1041no—
496C4—1042no—
497C4#1171869614yes—
498C4#1171930511yescharacteristic
499C4#1171932111yescharacteristic
500C4#1171932311yescharacteristic
501C4#1171932411yescharacteristic
502C2—82no—
503C2—82no—
504C2#1311832411yescharacteristic
505C2C2×#1171869611yescharacteristic
506C2#1312482111yescharacteristic
507C2#1312675811yescharacteristic
508C2#1312676411yescharacteristic
509C2#1312706711yescharacteristic
510C2#1312715711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#2537C2
socleC23×C13C22×D4
hypercenter#2537D13
hypocenterC13#24966
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #13117785C2semidirect
2. #13116273C2semidirect
3. #13116022C2semidirect
4. #13115631C2semidirect
5. #13115597C2semidirect
6. #13115159C2semidirect
7. #13114963C2semidirect
8. #13114928C2semidirect
9. #13114836C2semidirect
10. C4×#88072C2semidirect
409. C13#24966semidirect

Maximal subgroups

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

subgroupindex
#131177852
#131162732
#131160222
#131156312
#131155972
#131151592
#131149632
#131149282
#131148362
C4×#880722
C13×#25372
#2496613