Finite Group Databasebeta

← #14739243

Subgroups — #14739243

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079744C211yesmaximal, characteristic, complemented
2#13078071C211yesmaximal, characteristic
3#13077727C211yesmaximal, characteristic, complemented
4#13068034C212yesmaximal, complemented
5#13068027C212yesmaximal, complemented
6#13068000C212yesmaximal, complemented
7#13067993C212yesmaximal, complemented
8#13067388C211yesmaximal, characteristic, complemented
9#13067294C211yesmaximal, characteristic, complemented
10C2×#10622184C211yesmaximal, characteristic, complemented
11C11×#3079C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C4×C11×#41C2211yescharacteristic
14C2×#67003—21no—
15#10623008C2211yescharacteristic
16C11×#477C2212yes—
17C11×#476C2212yes—
18C11×#475—21no—
19C11×#474—21no—
20C11×#428—21no—
21C11×#423C2211yescharacteristic
22C11×#417—21no—
23#10622701C2212yes—
24#10622697—21no—
25#10622697—21no—
26#10622692C2212yes—
27#10622644C2211yescharacteristic
28#10622641—21no—
29#10622640C2211yescharacteristic
30Q8×C11⋊C8C2212yes—
31#10622632C2211yescharacteristic
32#10622629—21no—
33#10622628C2211yescharacteristic
34D4×C11⋊C8—22no—
35D4×C11⋊C8C2212yes—
36#10622615—21no—
37#10622581—22no—
38#10622538—21no—
39#10622538C2211yescharacteristic
40C2×C4⋊(C11⋊C8)—21no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622184C2212yes—
44#10622184C2212yes—
45#10622123C2212yes—
46#10622120C2212yes—
47#10622118C2212yes—
48#10622118C2212yes—
49C2×C11×#41D411yescharacteristic
50C22×Q8×C11—21no—
51C2×#4339—21no—
52C2×C11×M16—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2312yes—
57C4×Q8×C11D411yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11D411yescharacteristic
62C4×D4×C11C2311yescharacteristic
63C11×#117—21no—
64C11×#117D411yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69#67003—44no—
70C2×#4326—21no—
71C2×#4325—21no—
72C2×#4324—21no—
73C2×#4323—21no—
74#66983—21no—
75#66983—21no—
76C22×C11⋊C8—21no—
77C22×C11⋊C8—21no—
78C22×C11⋊C8—22no—
79#66928—21no—
80#66927C2311yescharacteristic
81C4×D44—21no—
82C4×D44—21no—
83#66922C2311yescharacteristic
84C11×#107—22no—
85C11×#106—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2312yes—
88C11×#103—22no—
89C11×#102—22no—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)D412yes—
92#66874—21no—
93#66874—21no—
94#66873—21no—
95#66873—21no—
96#66873—22no—
97#66873—22no—
98#66872—22no—
99#66872—22no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—22no—
103C4⋊(C11⋊C8)D411yescharacteristic
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2312yes—
110#19414—111nomaximal, Sylow
111C11×#41—22no—
112C11×#41SD1614yes—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—82no—
116C2×Q8×C11C2×D411yescharacteristic
117C2×D4×C11—21no—
118C2×D4×C11C2×D411yescharacteristic
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—41no—
127#4339—42no—
128#4339—42no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×C4×D11—41no—
133C2×Dic22—21no—
134C11×M16—42no—
135C2×C8×C11—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4C2×D411yescharacteristic
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11#4111yescharacteristic
153C42×C11C2411yescharacteristic
154#4326—42no—
155#4325—42no—
156#4324—42no—
157#4323—42no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—42no—
166C2×C11⋊C8—81no—
167C2×C11⋊C8—82no—
168C2×C11⋊C8C2×D412yes—
169C2×C11⋊C8C2×D412yes—
170#3227—111no—
171#3079D1111yescharacteristic, complemented
172#3035—111no—
173#2988—111no—
174#1678—112no—
175#1677—112no—
176#1672—112no—
177#1671—112no—
178#1570—111no—
179#1547—111no—
180C2×#333—111no—
181C23×C11—21no—
182C23×C11#12111yescharacteristic
183C22×D11—41no—
184Q8×C11—21no—
185Q8×C11—82no—
186Q8×C11—82no—
187Q8×C11C2×SD1612yes—
188D4×C11—24no—
189D4×C11—21no—
190D4×C11C2×SD1612yes—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—24no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—81no—
202C2×C4×C11—82no—
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11C2×SD1612yes—
207C2×C4×C11#13512yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C22⋊D11—82no—
212C2×Dic11—41no—
213D44—41no—
214D44—41no—
215D44—41no—
216D44—41no—
217D44—81no—
218C4×D11—82no—
219Dic22—41no—
220Dic22—41no—
221C8×C11—42no—
222C11⋊C8—22no—
223C11⋊C8—22no—
224C11⋊C8—41no—
225C11⋊C8—41no—
226C11⋊C8—42no—
227C2×#135—221no—
228#532—111no—
229C2×C4⋊Q8C2×D1111yescharacteristic
230C4×#41C2×D1111yescharacteristic
231#498—112no—
232#486—112no—
233#481—222no—
234#477C2×D1112yes—
235#476—221no—
236#476—221no—
237#476C2×D1112yes—
238#475—21no—
239#474—21no—
240#464—221no—
241#463—221no—
242#462—111no—
243#461—111no—
244#460—111no—
245#459—111no—
246C8×Q8—112no—
247C8×D4—112no—
248C8×D4—222no—
249#431—111no—
250#431—221no—
251#428—21no—
252#423C2×D1111yescharacteristic
253C2×C4⋊C8—111no—
254C2×C4⋊C8—111no—
255C2×C4⋊C8—221no—
256#417—21no—
257#416—221no—
258#334—112no—
259#334—112no—
260#333—112no—
261#333—112no—
262#332—112no—
263#331—112no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11#46512yes—
270C22×C11C2×#12111yescharacteristic
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—82no—
281C4×C11#46512yes—
282C4×C11C22×SD1611yescharacteristic
283C4×C11C2×#13511yescharacteristic
284C4×C11#57711yescharacteristic
285C4×C11#57811yescharacteristic
286Dic11—81no—
287C2×#41—221no—
288C2×#41C22⋊D1111yescharacteristic
289C22×Q8—21no—
290#135—444no—
291C2×Q16—221no—
292C2×SD16—221no—
293C2×SD16—221no—
294C2×D8—221no—
295C2×M16—21no—
296C22×C8—222no—
297C22×C8—221no—
298C22×C8—221no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—111no—
303C4⋊Q8C22×D1112yes—
304#127—111no—
305#124—221no—
306#121—221no—
307#121—221no—
308C4×Q8C22⋊D1111yescharacteristic
309C4×Q8C22×D1111yescharacteristic
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4C22⋊D1111yescharacteristic
315C4×D4C22×D1111yescharacteristic
316#117—21no—
317#117C22⋊D1111yescharacteristic
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C42—21no—
321C2×C42C22×D1111yescharacteristic
322#107—22no—
323#106—22no—
324#106—222no—
325#106—222no—
326C4⋊C8—21no—
327C4⋊C8—111no—
328C4⋊C8—111no—
329C4⋊C8—112no—
330C4⋊C8—111no—
331C4⋊C8—111no—
332C4⋊C8—222no—
333C4⋊C8—221no—
334C4⋊C8—221no—
335C4⋊C8C22×D1112yes—
336#103—22no—
337#103—221no—
338#103—221no—
339#102—22no—
340#102—222no—
341#102—222no—
342#102—221no—
343#102—221no—
344C22⋊C8—112no—
345C22⋊C8—222no—
346C4×C8—112no—
347C4×C8—222no—
348C2×C11—22no—
349C2×C11—42no—
350C2×C11#304611yescharacteristic
351C2×C11C2×#46511yescharacteristic
352C2×C11#306811yescharacteristic
353D11—161no—
354#41—22no—
355#41—442no—
356#41—442no—
357#41#432514yes—
358C2×Q8—22no—
359C2×Q8—41no—
360C2×Q8—82no—
361C2×Q8—221no—
362C2×Q8C2×C22⋊D1111yescharacteristic
363C2×D4—21no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—441no—
368C2×D4C2×C22⋊D1111yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—441no—
374C22×C4D4×D1111yescharacteristic
375C22×C4#434111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—442no—
378SD16—442no—
379SD16—442no—
380D8—442no—
381M16—42no—
382C2×C8—22no—
383C2×C8—112no—
384C2×C8—112no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—442no—
389C2×C8—882no—
390C2×C8—881no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4C2×C22⋊D1111yescharacteristic
400C4⋊C4C2×C22⋊D1111yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42D4×D1111yescharacteristic
410C42#434111yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C23×D1111yescharacteristic
413C11#1941411yescharacteristic, complemented, Sylow
414C23—21no—
415C23—441no—
416C23#6699211yescharacteristic
417Q8—21no—
418Q8—82no—
419Q8—82no—
420Q8—441no—
421Q8—441no—
422Q8C2×#432512yes—
423D4—24no—
424D4—21no—
425D4—441no—
426D4—441no—
427D4—441no—
428D4—441no—
429D4—881no—
430D4—882no—
431D4C2×#432512yes—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—441no—
445C2×C4—882no—
446C2×C4#6699211yescharacteristic
447C2×C4#6699211yescharacteristic
448C2×C4#6699211yescharacteristic
449C2×C4C2×#432512yes—
450C2×C4#6700312yes—
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4C22×C22⋊D1111yescharacteristic
454C8—42no—
455C8—222no—
456C8—222no—
457C8—442no—
458C8—441no—
459C8—441no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—881no—
466C22—881no—
467C22—881no—
468C22#1062266112yes—
469C22C2×#6699211yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—82no—
477C4—881no—
478C4#1062266112yes—
479C4#1062330911yescharacteristic
480C4#1062331011yescharacteristic
481C4C22×#432511yescharacteristic
482C4C2×#6700311yescharacteristic
483C2—22no—
484C2—42no—
485C2—1761no—
486C2#1307817011yescharacteristic
487C2C2×#1062266111yescharacteristic
488C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3079C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#3079D11
hypocenterC11#19414
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #13079744C2semidirect
3. #13077727C2semidirect
4. #13068034C2semidirect
5. #13068027C2semidirect
6. #13068000C2semidirect
7. #13067993C2semidirect
8. #13067388C2semidirect
9. #13067294C2semidirect
10. C2×#10622184C2semidirect
11. C11×#3079C2semidirect
171. #3079D11semidirect
413. C11#19414semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130780712
#130777272
#130680342
#130680272
#130680002
#130679932
#130673882
#130672942
C2×#106221842
C11×#30792
#1941411