Finite Group Databasebeta

← #15907790

Subgroups — #15907790

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#13117785C211yesmaximal, characteristic
2#13116262C212yesmaximal, complemented
3#13116036C212yesmaximal, complemented
4#13115631C211yesmaximal, characteristic
5#13115592C211yesmaximal, characteristic, complemented
6#13115149C212yesmaximal, complemented
7#13114963C211yesmaximal, characteristic, complemented
8#13114928C212yesmaximal, complemented
9#13114841C211yesmaximal, characteristic, complemented
10C4×#88075C211yesmaximal, characteristic, complemented
11C13×#2538C211yesmaximal, characteristic
12C2×C13×C22⋊Q8C2212yes—
13C2×C4×Q8×C13C2211yescharacteristic
14C2×C4×D4×C13C2211yescharacteristic
15C2×#88180C2212yes—
16C13×#396—22no—
17C13×#390—21no—
18C13×#389—21no—
19C13×#384C2211yescharacteristic
20C13×#380C2212yes—
21C2×#88075C2211yescharacteristic
22C2×#88075C2211yescharacteristic
23C2×#88075C2212yes—
24#11718882—21no—
25#11718873C2212yes—
26C2×C22⋊#1055C2212yes—
27C2×C22⋊#1055C2212yes—
28C4⋊C4×Dic13—21no—
29C2×#88047C2212yes—
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×Q8×C13C2311yescharacteristic
42C22×D4×C13D411yescharacteristic
43C23×C4×C13C2312yes—
44C13×C22⋊Q8—24no—
45C13×C22⋊Q8—42no—
46C4×Q8×C13—22no—
47C4×Q8×C13—22no—
48C4×D4×C13—22no—
49C4×D4×C13—22no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C4⋊C4C2311yescharacteristic
56C2×C13×C4⋊C4C2312yes—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4D412yes—
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62C2×C22⋊Dic13—22no—
63C2×C22⋊Dic13—22no—
64#88180—24no—
65#88180—42no—
66C2×C4⋊Dic13—21no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13C2312yes—
69C2×C4⋊Dic13C2311yescharacteristic
70C2×C4⋊Dic13C2311yescharacteristic
71C2×C4×Dic13—22no—
72C2×C4×Dic13—21no—
73C22×#1055C2311yescharacteristic
74C22×#1055C2311yescharacteristic
75C22×#1055C2312yes—
76C13×#95—22no—
77#88075—22no—
78#88075—22no—
79#88075—42no—
80#88071—21no—
81#88071—22no—
82C22⋊#1055—42no—
83C22⋊#1055—42no—
84#88047—42no—
85C4⋊#1055—22no—
86C4×#1055—22no—
87#24970—131nomaximal, Sylow
88C24×C13C2×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—
95C2×D4×C13—22no—
96C2×D4×C13—22no—
97C2×D4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13C2×D412yes—
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2411yescharacteristic
111C22×Dic13—21no—
112C22×Dic13—21no—
113C22×Dic13—22no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—22no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—44no—
120C13×C4⋊C4—42no—
121C13×C4⋊C4—42no—
122C13×C4⋊C4—81no—
123C13×C22⋊C4—24no—
124C13×C22⋊C4—44no—
125C13×C22⋊C4—82no—
126C42×C13—42no—
127C42×C13#4112yes—
128C42×C13#4112yes—
129C22⋊Dic13—44no—
130C22⋊Dic13—82no—
131C4⋊Dic13—21no—
132C4⋊Dic13—21no—
133C4⋊Dic13—22no—
134C4⋊Dic13—22no—
135C4⋊Dic13—21no—
136C4⋊Dic13—42no—
137C4⋊Dic13—81no—
138C4⋊Dic13#4112yes—
139C4×Dic13—44no—
140C4×Dic13—42no—
141C2×#1055—21no—
142C2×#1055—21no—
143C2×#1055—21no—
144C2×#1055—21no—
145C2×#1055—22no—
146C2×#1055—21no—
147C2×#1055—21no—
148C2×#1055—22no—
149C2×#1055—22no—
150#2538D1311yescharacteristic
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#1803—131no—
160C4×#103—131no—
161C23×C13—22no—
162C23×C13—22no—
163C23×C13—22no—
164C23×C13—22no—
165C23×C13—22no—
166C23×C13—22no—
167C23×C13—22no—
168C23×C13C22×D411yescharacteristic
169Q8×C13—22no—
170Q8×C13—22no—
171Q8×C13—41no—
172Q8×C13—41no—
173D4×C13—44no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—22no—
177C2×C4×C13—22no—
178C2×C4×C13—22no—
179C2×C4×C13—22no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—42no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13—42no—
189C2×C4×C13—41no—
190C2×C4×C13—42no—
191C2×C4×C13—41no—
192C2×C4×C13#12312yes—
193C2×C4×C13#12312yes—
194C2×C4×C13#13512yes—
195C2×C4×C13#13712yes—
196C2×C4×C13C2×#4111yescharacteristic
197C2×C4×C13C2×#4111yescharacteristic
198C2×C4×C13C2×#4111yescharacteristic
199C2×C4×C13C2×#4111yescharacteristic
200C2×C4×C13H(5,𝔽2)11yescharacteristic
201C2×C4×C13H(5,𝔽2)11yescharacteristic
202C2×Dic13—22no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205C2×Dic13—42no—
206C2×Dic13—41no—
207C2×Dic13—41no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—41no—
211#1055—42no—
212#1055—41no—
213#1055—41no—
214C2×C22⋊Q8C2×D1312yes—
215C2×C4×Q8C2×D1311yescharacteristic
216C2×C4×D4C2×D1311yescharacteristic
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×C8—131no—
226#396—22no—
227#390—21no—
228#390—261no—
229#389—21no—
230#388—262no—
231#384—131no—
232#384C2×D1311yescharacteristic
233#380—132no—
234#380C2×D1312yes—
235C4×C4⋊C4—131no—
236C4×C4⋊C4—261no—
237#340—132no—
238#340—131no—
239#340—132no—
240#340—131no—
241#340—132no—
242#340—132no—
243C22×C13—42no—
244C22×C13—42no—
245C22×C13—42no—
246C22×C13—42no—
247C22×C13—42no—
248C22×C13—42no—
249C22×C13—42no—
250C22×C13C2×#12311yescharacteristic
251C22×C13#54611yescharacteristic
252C22×C13#54611yescharacteristic
253C22×C13C2×#13511yescharacteristic
254C22×C13C2×#13711yescharacteristic
255C22×C13#57611yescharacteristic
256C22×C13#57811yescharacteristic
257C4×C13—22no—
258C4×C13—42no—
259C4×C13—42no—
260C4×C13—81no—
261C4×C13—82no—
262C4×C13#48514yes—
263C4×C13#52911yescharacteristic
264C4×C13#54011yescharacteristic
265C4×C13#55311yescharacteristic
266C4×C13#55511yescharacteristic
267Dic13—42no—
268Dic13—82no—
269Dic13—81no—
270C22×Q8C22×D1311yescharacteristic
271C22×D4C22⋊D1311yescharacteristic
272C23×C4C22×D1312yes—
273C22×C8—131no—
274C22×C8—131no—
275C22×C8—132no—
276C22⋊Q8—24no—
277C22⋊Q8—42no—
278C4×Q8—22no—
279C4×Q8—22no—
280C4×D4—22no—
281C4×D4—22no—
282#117—264no—
283#117—522no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—131no—
289C2×C4⋊C4—132no—
290C2×C4⋊C4—131no—
291C2×C4⋊C4—261no—
292C2×C4⋊C4—261no—
293C2×C4⋊C4C22⋊D1311yescharacteristic
294C2×C4⋊C4C22×D1311yescharacteristic
295C2×C4⋊C4C22×D1312yes—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—262no—
299C2×C22⋊C4—262no—
300C2×C22⋊C4C22⋊D1312yes—
301C2×C42—21no—
302C2×C42—262no—
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—262no—
313#95—22no—
314#95—261no—
315#95—262no—
316C2×C13—82no—
317C2×C13#242011yescharacteristic
318C2×C13C2×#48511yescharacteristic
319C2×C13#309811yescharacteristic
320C2×C13#330211yescharacteristic
321C2×C13#330511yescharacteristic
322C2×C13#332811yescharacteristic
323C2×C13#333311yescharacteristic
324C24C2×C22⋊D1312yes—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8#612912yes—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—261no—
344C22×C4—261no—
345C22×C4—262no—
346C22×C4C2×C22⋊D1312yes—
347C22×C4C2×C22⋊D1311yescharacteristic
348C22×C4C2×C22⋊D1311yescharacteristic
349C22×C4C23×D1311yescharacteristic
350C2×C8—261no—
351C2×C8—261no—
352C2×C8—261no—
353C2×C8—262no—
354C2×C8—261no—
355C2×C8—262no—
356C2×C8—261no—
357C2×C8—261no—
358C2×C8—262no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—44no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—81no—
368C4⋊C4—132no—
369C4⋊C4—261no—
370C4⋊C4—261no—
371C4⋊C4—261no—
372C4⋊C4—262no—
373C4⋊C4—262no—
374C4⋊C4—522no—
375C4⋊C4—1041no—
376C22⋊C4—24no—
377C22⋊C4—44no—
378C22⋊C4—82no—
379C22⋊C4—524no—
380C22⋊C4—1042no—
381C42—42no—
382C42—524no—
383C42—522no—
384C42#612912yes—
385C42#612912yes—
386C13#2497011yescharacteristic, complemented, Sylow
387C23—22no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23C22×C22⋊D1311yescharacteristic
395Q8—22no—
396Q8—22no—
397Q8—41no—
398Q8—41no—
399D4—44no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—262no—
419C2×C4—521no—
420C2×C4—521no—
421C2×C4—521no—
422C2×C4—522no—
423C2×C4—521no—
424C2×C4—522no—
425C2×C4—521no—
426C2×C4—522no—
427C2×C4#8818912yes—
428C2×C4#8818912yes—
429C2×C4#8819612yes—
430C2×C4#8820412yes—
431C2×C4C2×#612911yescharacteristic
432C2×C4C2×#612911yescharacteristic
433C2×C4C2×#612911yescharacteristic
434C2×C4#8825111yescharacteristic
435C2×C4#41×D1311yescharacteristic
436C2×C4#8825611yescharacteristic
437C8—521no—
438C8—521no—
439C8—522no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22C2×#8818911yescharacteristic
448C22#1171951111yescharacteristic
449C22C2×#8819611yescharacteristic
450C22C2×#8820411yescharacteristic
451C22#1171953411yescharacteristic
452C22#1171954011yescharacteristic
453C22#1171954311yescharacteristic
454C4—22no—
455C4—42no—
456C4—42no—
457C4—82no—
458C4—81no—
459C4—522no—
460C4—1042no—
461C4—1041no—
462C4#1171870614yes—
463C4#1171930511yescharacteristic
464C4#1171932111yescharacteristic
465C4#1171932311yescharacteristic
466C4#1171932411yescharacteristic
467C2—82no—
468C2#1311832411yescharacteristic
469C2C2×#1171870611yescharacteristic
470C2#1312481011yescharacteristic
471C2#1312674711yescharacteristic
472C2#1312678611yescharacteristic
473C2#1312711911yescharacteristic
474C2#1312716811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2538C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2538D13
hypocenterC13#24970
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. #13116262C2semidirect
3. #13116036C2semidirect
5. #13115592C2semidirect
6. #13115149C2semidirect
7. #13114963C2semidirect
8. #13114928C2semidirect
9. #13114841C2semidirect
10. C4×#88075C2semidirect
386. C13#24970semidirect

Maximal subgroups

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

subgroupindex
#131177852
#131162622
#131160362
#131156312
#131155922
#131151492
#131149632
#131149282
#131148412
C4×#880752
C13×#25382
#2497013