Finite Group Databasebeta

← #15907796

Subgroups — #15907796

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119754C211yesmaximal, characteristic
2#13117787C211yesmaximal, characteristic
3#13116261C212yesmaximal, complemented
4#13116038C212yesmaximal, complemented
5#13115629C211yesmaximal, characteristic
6#13115595C211yesmaximal, characteristic, complemented
7#13115145C212yesmaximal, complemented
8#13114963C211yesmaximal, characteristic, complemented
9#13114930C212yesmaximal, complemented
10C4×#88075C211yesmaximal, characteristic, complemented
11C13×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C13C2211yescharacteristic
13C2×#88200C2212yes—
14C2×#88146C2212yes—
15C2×C4×D52C2211yescharacteristic
16C2×C13×C4⋊C8C2211yescharacteristic
17C2×C13×#103C2212yes—
18C13×#384C2211yescharacteristic
19C2×#88075C2211yescharacteristic
20C2×#88075C2211yescharacteristic
21C2×#88060C2212yes—
22C2×#88060C2212yes—
23C2×#88058C2212yes—
24#11718655—22no—
25#11718651—22no—
26#11718649—21no—
27#11718648C2212yes—
28#11718648C2212yes—
29C4⋊C4×Dic13—21no—
30#11718600—21no—
31#11718596C2211yescharacteristic
32C4×C4⋊Dic13C2211yescharacteristic
33#11718589—21no—
34C2×C4×#1055C2211yescharacteristic
35C13×#340C2212yes—
36#11718143C2212yes—
37#11718121C2212yes—
38#11718121C2211yescharacteristic
39#11718121C2211yescharacteristic
40#11718121C2212yes—
41C22×Q8×C13C2311yescharacteristic
42C22×D52D411yescharacteristic
43C22×C4×D13C2312yes—
44C22×C8×C13C2312yes—
45C4×Q8×C13—22no—
46C4×Q8×C13—22no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4C2312yes—
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C42×C13—21no—
53C2×C42×C13C2311yescharacteristic
54#88200—24no—
55#88200—42no—
56C2×#6103—22no—
57C2×#6103—22no—
58C2×#6103—22no—
59C2×#6103—22no—
60C2×#6103D412yes—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13—21no—
63C2×C4⋊Dic13D411yescharacteristic
64C2×C4⋊Dic13C2312yes—
65C2×C4⋊Dic13C2311yescharacteristic
66C2×C4⋊Dic13C2311yescharacteristic
67C2×#6101—22no—
68C2×C4×Dic13—21no—
69C2×C4×Dic13—22no—
70C22×#1055C2311yescharacteristic
71C22×#1055C2311yescharacteristic
72#88146—24no—
73#88146—42no—
74C4×D52—22no—
75C4×D52—22no—
76C13×C4⋊C8—22no—
77C13×#103—42no—
78#88075—22no—
79#88075—22no—
80#88071—21no—
81#88071—22no—
82#88071—22no—
83#88060—42no—
84#88060—42no—
85#88058—42no—
86C4×#1055—22no—
87#24970—131nomaximal, Sylow
88C23×D13C2×D412yes—
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—21no—
93C2×Q8×C13—21no—
94C2×Q8×C13#4112yes—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2411yescharacteristic
101C22×Dic13—21no—
102C22×Dic13—21no—
103C22×Dic13—22no—
104C22×Dic13C2×D412yes—
105C2×D52—22no—
106C2×D52—22no—
107C2×D52—22no—
108C2×C4×D13—22no—
109C2×C4×D13—22no—
110C2×C4×D13—22no—
111C2×C4×D13—22no—
112C2×C4×D13—22no—
113C2×C4×D13—22no—
114C2×C8×C13—22no—
115C2×C8×C13—22no—
116C2×C8×C13—22no—
117C13×C4⋊C4—22no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—42no—
122C13×C4⋊C4—42no—
123C13×C4⋊C4—81no—
124C42×C13—42no—
125C42×C13#4112yes—
126C42×C13#4112yes—
127#6103—24no—
128#6103—44no—
129#6103—44no—
130#6103—82no—
131#6103—82no—
132C4⋊Dic13—22no—
133C4⋊Dic13—21no—
134C4⋊Dic13—21no—
135C4⋊Dic13—22no—
136C4⋊Dic13—22no—
137C4⋊Dic13—21no—
138C4⋊Dic13—42no—
139C4⋊Dic13—81no—
140C4⋊Dic13#4112yes—
141#6101—44no—
142C4×Dic13—44no—
143C4×Dic13—42no—
144C2×#1055—21no—
145C2×#1055—21no—
146C2×#1055—21no—
147C2×#1055—21no—
148C2×#1055—21no—
149C2×#1055—21no—
150#2538—131no—
151#2354—131no—
152#2075—132no—
153#2036—132no—
154#1954—131no—
155#1947—131no—
156#1873—132no—
157#1834—131no—
158#1825—132no—
159#1803D1311yescharacteristic, complemented
160C4×#103—131no—
161C23×C13C22×D411yescharacteristic
162C22×D13—22no—
163C22×D13—22no—
164C22×D13—22no—
165C22×D13—22no—
166C22×D13—22no—
167C22×D13—22no—
168C22×D13—22no—
169Q8×C13—22no—
170Q8×C13—22no—
171Q8×C13—41no—
172Q8×C13—41no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—22no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—42no—
180C2×C4×C13—42no—
181C2×C4×C13—41no—
182C2×C4×C13—42no—
183C2×C4×C13—41no—
184C2×C4×C13#12312yes—
185C2×C4×C13#12312yes—
186C2×C4×C13#13512yes—
187C2×C4×C13#13712yes—
188C2×C4×C13C2×#4111yescharacteristic
189C2×C4×C13C2×#4111yescharacteristic
190C2×C4×C13C2×#4111yescharacteristic
191C2×C4×C13C2×#4111yescharacteristic
192C2×C4×C13H(5,𝔽2)11yescharacteristic
193C2×C4×C13H(5,𝔽2)11yescharacteristic
194C2×Dic13—22no—
195C2×Dic13—22no—
196C2×Dic13—22no—
197C2×Dic13—22no—
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—42no—
201C2×Dic13—41no—
202C2×Dic13—41no—
203C2×Dic13—42no—
204C2×Dic13—42no—
205C2×Dic13—41no—
206D52—44no—
207C4×D13—42no—
208C4×D13—42no—
209C4×D13—42no—
210C4×D13—42no—
211C8×C13—42no—
212#1055—41no—
213#1055—41no—
214C2×C22⋊Q8—132no—
215C2×C4×Q8C2×D1311yescharacteristic
216C2×C4×D4—131no—
217C2×#117—132no—
218C2×#107—132no—
219C2×C4⋊C8C2×D1311yescharacteristic
220C2×#103—131no—
221C2×#103—131no—
222C2×#103C2×D1312yes—
223C2×C22⋊C8—132no—
224C2×C22⋊C8—132no—
225C2×C4×C8—131no—
226#396—262no—
227#390—261no—
228#390—261no—
229#389—261no—
230#388—262no—
231#384—131no—
232#384C2×D1311yescharacteristic
233#380—132no—
234#380—132no—
235C4×C4⋊C4—131no—
236C4×C4⋊C4—261no—
237#340—132no—
238#340—131no—
239#340—132no—
240#340—131no—
241#340—132no—
242#340C2×D1312yes—
243C22×C13C2×#12311yescharacteristic
244C22×C13#54611yescharacteristic
245C22×C13#54611yescharacteristic
246C22×C13C2×#13511yescharacteristic
247C22×C13C2×#13711yescharacteristic
248C22×C13#57611yescharacteristic
249C22×C13#57811yescharacteristic
250C2×D13—42no—
251C2×D13—42no—
252C2×D13—42no—
253C2×D13—42no—
254C2×D13—42no—
255C2×D13—42no—
256C2×D13—42no—
257C4×C13—22no—
258C4×C13—42no—
259C4×C13—82no—
260C4×C13—81no—
261C4×C13#48514yes—
262C4×C13#52911yescharacteristic
263C4×C13#54011yescharacteristic
264C4×C13#55311yescharacteristic
265C4×C13#55511yescharacteristic
266Dic13—42no—
267Dic13—42no—
268Dic13—82no—
269Dic13—81no—
270C22×Q8C22×D1311yescharacteristic
271C22×D4—131no—
272C23×C4—132no—
273C22×C8—131no—
274C22×C8—131no—
275C22×C8C22×D1312yes—
276C22⋊Q8—264no—
277C22⋊Q8—522no—
278C4×Q8—22no—
279C4×Q8—22no—
280C4×D4—262no—
281C4×D4—262no—
282#117—264no—
283#117—522no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—131no—
288C2×C4⋊C4—131no—
289C2×C4⋊C4—132no—
290C2×C4⋊C4—131no—
291C2×C4⋊C4—262no—
292C2×C4⋊C4—261no—
293C2×C4⋊C4—261no—
294C2×C4⋊C4C22×D1312yes—
295C2×C4⋊C4C22×D1311yescharacteristic
296C2×C22⋊C4—132no—
297C2×C22⋊C4—262no—
298C2×C22⋊C4—262no—
299C2×C22⋊C4—262no—
300C2×C22⋊C4—262no—
301C2×C42—21no—
302C2×C42—262no—
303C2×C42—261no—
304C2×C42C22×D1311yescharacteristic
305#107—522no—
306C4⋊C8—22no—
307#103—42no—
308#103—262no—
309#103—262no—
310C22⋊C8—522no—
311C22⋊C8—522no—
312C4×C8—262no—
313#95—262no—
314#95—262no—
315#95—261no—
316C2×C13#242011yescharacteristic
317C2×C13C2×#48511yescharacteristic
318C2×C13#309811yescharacteristic
319C2×C13#330211yescharacteristic
320C2×C13#330511yescharacteristic
321C2×C13#332811yescharacteristic
322C2×C13#333311yescharacteristic
323D13—82no—
324C24—132no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8#613112yes—
331C2×D4—262no—
332C2×D4—262no—
333C2×D4—262no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—132no—
338C22×C4—261no—
339C22×C4—262no—
340C22×C4—262no—
341C22×C4—262no—
342C22×C4—262no—
343C22×C4—262no—
344C22×C4—262no—
345C22×C4—261no—
346C22×C4—262no—
347C22×C4D4×D1311yescharacteristic
348C22×C4D4×D1311yescharacteristic
349C22×C4C23×D1311yescharacteristic
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—261no—
354C2×C8—261no—
355C2×C8—261no—
356C2×C8—261no—
357C2×C8—261no—
358C2×C8—261no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—81no—
366C4⋊C4—132no—
367C4⋊C4—262no—
368C4⋊C4—261no—
369C4⋊C4—261no—
370C4⋊C4—262no—
371C4⋊C4—261no—
372C4⋊C4—262no—
373C4⋊C4—524no—
374C4⋊C4—522no—
375C4⋊C4—1041no—
376C22⋊C4—264no—
377C22⋊C4—524no—
378C22⋊C4—524no—
379C22⋊C4—1042no—
380C22⋊C4—1042no—
381C42—42no—
382C42—524no—
383C42—522no—
384C42#612712yes—
385C42#612912yes—
386C13#2497011yescharacteristic, complemented, Sylow
387C23—262no—
388C23—262no—
389C23—262no—
390C23—262no—
391C23—262no—
392C23—262no—
393C23—262no—
394C23C2×D4×D1311yescharacteristic
395Q8—22no—
396Q8—22no—
397Q8—41no—
398Q8—41no—
399D4—524no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—262no—
412C2×C4—262no—
413C2×C4—262no—
414C2×C4—262no—
415C2×C4—521no—
416C2×C4—521no—
417C2×C4—522no—
418C2×C4—522no—
419C2×C4—522no—
420C2×C4—522no—
421C2×C4—521no—
422C2×C4—522no—
423C2×C4—521no—
424C2×C4—522no—
425C2×C4—522no—
426C2×C4—521no—
427C2×C4#8813712yes—
428C2×C4#8813712yes—
429C2×C4#8816912yes—
430C2×C4#8817312yes—
431C2×C4C2×#612711yescharacteristic
432C2×C4C2×#612911yescharacteristic
433C2×C4#8825111yescharacteristic
434C2×C4C2×#613111yescharacteristic
435C2×C4#41×D1311yescharacteristic
436C2×C4#8825611yescharacteristic
437C8—42no—
438C8—521no—
439C8—521no—
440C22—522no—
441C22—522no—
442C22—522no—
443C22—522no—
444C22—522no—
445C22—522no—
446C22—522no—
447C22C2×#8813711yescharacteristic
448C22#1171931711yescharacteristic
449C22#1171933511yescharacteristic
450C22C2×#8816911yescharacteristic
451C22C2×#8817311yescharacteristic
452C22#1171947911yescharacteristic
453C22#1171948411yescharacteristic
454C4—22no—
455C4—42no—
456C4—82no—
457C4—81no—
458C4—522no—
459C4—522no—
460C4—1041no—
461C4—1042no—
462C4#1171847514yes—
463C4#1171921911yescharacteristic
464C4#1171923711yescharacteristic
465C4#1171932411yescharacteristic
466C4#1171932911yescharacteristic
467C2—1042no—
468C2#1311833011yescharacteristic
469C2C2×#1171847511yescharacteristic
470C2#1312481311yescharacteristic
471C2#1312675611yescharacteristic
472C2#1312678311yescharacteristic
473C2#1312711611yescharacteristic
474C2#1312717711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1803C2
socleC23×C13C22×D4
prime radicalC22×D52D4
hypercenter#1803D13
hypocenterC13#24970
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
3. #13116261C2semidirect
4. #13116038C2semidirect
6. #13115595C2semidirect
7. #13115145C2semidirect
8. #13114963C2semidirect
9. #13114930C2semidirect
10. C4×#88075C2semidirect
11. C13×#1803C2semidirect
159. #1803D13semidirect
386. C13#24970semidirect

Maximal subgroups

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

subgroupindex
#131197542
#131177872
#131162612
#131160382
#131156292
#131155952
#131151452
#131149632
#131149302
C4×#880752
C13×#18032
#2497013