Finite Group Databasebeta

← #15907797

Subgroups — #15907797

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#13119759C211yesmaximal, characteristic
2#13117787C211yesmaximal, characteristic
3#13116263C212yesmaximal, complemented
4#13116042C212yesmaximal, complemented
5#13115630C211yesmaximal, characteristic
6#13115592C211yesmaximal, characteristic, complemented
7#13115147C212yesmaximal, complemented
8#13114930C212yesmaximal, complemented
9#13114838C211yesmaximal, characteristic, complemented
10C4×#88056C211yesmaximal, characteristic, complemented
11C13×#1834C211yesmaximal, characteristic, complemented
12C2×#88151C2212yes—
13C2×#88146C2212yes—
14C2×C4×D52C2211yescharacteristic
15C2×C4×Dic26C2211yescharacteristic
16C2×C4×C8×C13C2211yescharacteristic
17C13×#384C2211yescharacteristic
18C13×#384C2211yescharacteristic
19C2×#88060C2212yes—
20C2×#88060C2212yes—
21C2×#88056C2211yescharacteristic
22C2×#88056C2211yescharacteristic
23#11718655—22no—
24#11718651—22no—
25#11718649—21no—
26#11718649—21no—
27#11718648C2212yes—
28#11718648C2212yes—
29#11718646—21no—
30C4⋊C4×Dic13—21no—
31C2×#88050C2212yes—
32C2×#88047C2212yes—
33C4×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊#1055C2211yescharacteristic
35C13×#340C2212yes—
36C13×#340C2212yes—
37#11718143C2211yescharacteristic
38#11718143C2211yescharacteristic
39#11718121C2212yes—
40#11718121C2212yes—
41C22×D52D411yescharacteristic
42C22×C4×D13C2312yes—
43C22×Dic26C2311yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C22×C8×C13C2311yescharacteristic
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4C2312yes—
51C2×C13×C4⋊C4C2312yes—
52C2×C42×C13C2311yescharacteristic
53C2×#6103—22no—
54C2×#6103—22no—
55C2×#6103—22no—
56C2×#6103—22no—
57C2×#6103D412yes—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13D411yescharacteristic
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4⋊Dic13C2311yescharacteristic
63C2×#6101—21no—
64C2×C4×Dic13—21no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13—22no—
67C22×#1055C2312yes—
68#88151—24no—
69#88151—42no—
70#88146—24no—
71#88146—42no—
72C4×D52—22no—
73C4×D52—22no—
74C4×Dic26—22no—
75C4×Dic26—22no—
76C4×C8×C13—22no—
77#88071—21no—
78#88071—22no—
79#88071—22no—
80#88060—42no—
81#88060—42no—
82#88056—22no—
83#88056—22no—
84#88050—42no—
85#88047—42no—
86C4⋊#1055—22no—
87#24970—131nomaximal, Sylow
88C23×D13C2×D412yes—
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2411yescharacteristic
94C22×Dic13—21no—
95C22×Dic13—21no—
96C22×Dic13—21no—
97C22×Dic13—21no—
98C22×Dic13C2×D412yes—
99C2×D52—22no—
100C2×D52—22no—
101C2×D52—22no—
102C2×C4×D13—22no—
103C2×C4×D13—22no—
104C2×C4×D13—22no—
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13—22no—
108C2×Dic26—21no—
109C2×Dic26—21no—
110C2×Dic26—21no—
111C2×Dic26—21no—
112C2×Dic26—21no—
113C2×Dic26#4112yes—
114C2×C8×C13—21no—
115C2×C8×C13—21no—
116C2×C8×C13—21no—
117C2×C8×C13—21no—
118C2×C8×C13—21no—
119C2×C8×C13—21no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—42no—
125C13×C4⋊C4—42no—
126C13×C4⋊C4—81no—
127C13×C4⋊C4—81no—
128C42×C13#4112yes—
129C42×C13#4112yes—
130#6103—24no—
131#6103—44no—
132#6103—44no—
133#6103—82no—
134#6103—82no—
135C4⋊Dic13—22no—
136C4⋊Dic13—21no—
137C4⋊Dic13—21no—
138C4⋊Dic13—21no—
139C4⋊Dic13—21no—
140C4⋊Dic13—21no—
141C4⋊Dic13—44no—
142C4⋊Dic13#4112yes—
143#6101—42no—
144C4×Dic13—44no—
145C4×Dic13—42no—
146C4×Dic13—42no—
147C2×#1055—22no—
148C2×#1055—22no—
149C2×#1055—22no—
150#2538—131no—
151#2354—131no—
152#2075—132no—
153#2036—132no—
154#1954—131no—
155#1947—131no—
156#1873—132no—
157#1834D1311yescharacteristic, complemented
158#1825—132no—
159#1803—131no—
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—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13#12312yes—
178C2×C4×C13#12312yes—
179C2×C4×C13#13512yes—
180C2×C4×C13#13712yes—
181C2×C4×C13C2×#4111yescharacteristic
182C2×C4×C13C2×#4111yescharacteristic
183C2×C4×C13C2×#4111yescharacteristic
184C2×C4×C13C2×#4111yescharacteristic
185C2×C4×C13H(5,𝔽2)11yescharacteristic
186C2×C4×C13H(5,𝔽2)11yescharacteristic
187C2×Dic13—22no—
188C2×Dic13—22no—
189C2×Dic13—22no—
190C2×Dic13—22no—
191C2×Dic13—22no—
192C2×Dic13—41no—
193C2×Dic13—41no—
194C2×Dic13—41no—
195C2×Dic13—41no—
196C2×Dic13—41no—
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202D52—44no—
203C4×D13—42no—
204C4×D13—42no—
205C4×D13—42no—
206C4×D13—42no—
207Dic26—22no—
208Dic26—22no—
209Dic26—41no—
210Dic26—41no—
211C8×C13—41no—
212C8×C13—41no—
213#1055—42no—
214C2×C22⋊Q8—132no—
215C2×C4×Q8—131no—
216C2×C4×D4—131no—
217C2×#117—132no—
218C2×#107—132no—
219C2×C4⋊C8—131no—
220C2×#103—131no—
221C2×#103—131no—
222C2×#103—132no—
223C2×C22⋊C8—132no—
224C2×C22⋊C8—132no—
225C2×C4×C8C2×D1311yescharacteristic
226#396—262no—
227#390—261no—
228#390—261no—
229#389—261no—
230#388—262no—
231#384C2×D1311yescharacteristic
232#384C2×D1311yescharacteristic
233#380—132no—
234#380—132no—
235C4×C4⋊C4—131no—
236C4×C4⋊C4—261no—
237#340—131no—
238#340—131no—
239#340—132no—
240#340—132no—
241#340C2×D1312yes—
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—82no—
259C4×C13—82no—
260C4×C13#48514yes—
261C4×C13#52911yescharacteristic
262C4×C13#54011yescharacteristic
263C4×C13#55311yescharacteristic
264C4×C13#55511yescharacteristic
265Dic13—42no—
266Dic13—42no—
267Dic13—42no—
268Dic13—81no—
269Dic13—81no—
270C22×Q8—131no—
271C22×D4—131no—
272C23×C4—132no—
273C22×C8—132no—
274C22×C8C22×D1311yescharacteristic
275C22×C8C22×D1311yescharacteristic
276C22⋊Q8—264no—
277C22⋊Q8—522no—
278C4×Q8—262no—
279C4×Q8—262no—
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—21no—
288C2×C4⋊C4—131no—
289C2×C4⋊C4—131no—
290C2×C4⋊C4—131no—
291C2×C4⋊C4—131no—
292C2×C4⋊C4—262no—
293C2×C4⋊C4—261no—
294C2×C4⋊C4C22×D1312yes—
295C2×C4⋊C4C22×D1312yes—
296C2×C22⋊C4—132no—
297C2×C22⋊C4—262no—
298C2×C22⋊C4—262no—
299C2×C22⋊C4—262no—
300C2×C22⋊C4—262no—
301C2×C42—262no—
302C2×C42—261no—
303C2×C42—261no—
304C2×C42C22×D1311yescharacteristic
305#107—522no—
306C4⋊C8—262no—
307#103—262no—
308#103—262no—
309#103—522no—
310C22⋊C8—522no—
311C22⋊C8—522no—
312C4×C8—22no—
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—132no—
326C2×Q8—261no—
327C2×Q8—261no—
328C2×Q8—261no—
329C2×Q8—261no—
330C2×Q8—261no—
331C2×D4—262no—
332C2×D4—262no—
333C2×D4—262no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—132no—
337C22×C4—261no—
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—261no—
347C22×C4D4×D1311yescharacteristic
348C22×C4D4×D1311yescharacteristic
349C22×C4C23×D1311yescharacteristic
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—262no—
357C2×C8—262no—
358C2×C8—262no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—81no—
366C4⋊C4—81no—
367C4⋊C4—132no—
368C4⋊C4—262no—
369C4⋊C4—261no—
370C4⋊C4—261no—
371C4⋊C4—261no—
372C4⋊C4—261no—
373C4⋊C4—261no—
374C4⋊C4—524no—
375C4⋊C4—522no—
376C22⋊C4—264no—
377C22⋊C4—524no—
378C22⋊C4—524no—
379C22⋊C4—1042no—
380C22⋊C4—1042no—
381C42—524no—
382C42—522no—
383C42—522no—
384C42#612712yes—
385C42#613112yes—
386C13#2497011yescharacteristic, complemented, Sylow
387C23—262no—
388C23—262no—
389C23—262no—
390C23—262no—
391C23—262no—
392C23—262no—
393C23—262no—
394C23C2×D4×D1311yescharacteristic
395Q8—262no—
396Q8—262no—
397Q8—521no—
398Q8—521no—
399D4—524no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—262no—
409C2×C4—262no—
410C2×C4—262no—
411C2×C4—262no—
412C2×C4—262no—
413C2×C4—521no—
414C2×C4—521no—
415C2×C4—521no—
416C2×C4—521no—
417C2×C4—522no—
418C2×C4—522no—
419C2×C4—522no—
420C2×C4—522no—
421C2×C4—521no—
422C2×C4—521no—
423C2×C4—521no—
424C2×C4—521no—
425C2×C4—521no—
426C2×C4—521no—
427C2×C4#8814812yes—
428C2×C4#8814812yes—
429C2×C4#8816912yes—
430C2×C4#8817012yes—
431C2×C4C2×#612711yescharacteristic
432C2×C4C2×#613111yescharacteristic
433C2×C4#41×D1311yescharacteristic
434C2×C4#41×D1311yescharacteristic
435C2×C4#8825611yescharacteristic
436C2×C4#8825611yescharacteristic
437C8—41no—
438C8—41no—
439C8—522no—
440C22—522no—
441C22—522no—
442C22—522no—
443C22—522no—
444C22—522no—
445C22—522no—
446C22—522no—
447C22C2×#8814811yescharacteristic
448C22#1171938111yescharacteristic
449C22#1171938111yescharacteristic
450C22#1171946211yescharacteristic
451C22C2×#8816911yescharacteristic
452C22C2×#8817011yescharacteristic
453C22#1171947111yescharacteristic
454C4—22no—
455C4—82no—
456C4—82no—
457C4—522no—
458C4—522no—
459C4—522no—
460C4—1041no—
461C4—1041no—
462C4#1171852814yes—
463C4#1171923511yescharacteristic
464C4#1171923711yescharacteristic
465C4#1171939611yescharacteristic
466C4#1171940311yescharacteristic
467C2—1042no—
468C2#1311833111yescharacteristic
469C2C2×#1171852811yescharacteristic
470C2#1312481911yescharacteristic
471C2#1312675211yescharacteristic
472C2#1312678511yescharacteristic
473C2#1312711811yescharacteristic
474C2#1312717311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1834C2
socleC23×C13C22×D4
prime radicalC22×D52D4
hypercenter#1834D13
hypocenterC13#24970
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
3. #13116263C2semidirect
4. #13116042C2semidirect
6. #13115592C2semidirect
7. #13115147C2semidirect
8. #13114930C2semidirect
9. #13114838C2semidirect
10. C4×#88056C2semidirect
11. C13×#1834C2semidirect
157. #1834D13semidirect
386. C13#24970semidirect

Maximal subgroups

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

subgroupindex
#131197592
#131177872
#131162632
#131160422
#131156302
#131155922
#131151472
#131149302
#131148382
C4×#880562
C13×#18342
#2497013