Finite Group Databasebeta

← #14810753

Subgroups — #14810753

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic22C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic
3#13074105C211yesmaximal, characteristic
4#13069755C212yesmaximal, complemented
5#13069750C212yesmaximal
6#13069567C211yesmaximal, characteristic, complemented
7#13069555C211yesmaximal, characteristic, complemented
8#13068973C212yesmaximal
9#13068959C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#464C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×Q8×Dic11C2212yes—
17Q8×Dic22—24no—
18Q8×Dic22—24no—
19C2×#66941—22no—
20C2×#66941C2212yes—
21C2×#66922—21no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C11×#464—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29#10622843C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2212yes—
32#10622834C2212yes—
33C2×#66896C2212yes—
34#10622668—24no—
35#10622566—21no—
36#10622560—21no—
37#10622558—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C22×Dic22—21no—
49C22×Dic22—22no—
50C22×Dic22D411yescharacteristic
51C2×C11×Q16—22no—
52C2×C11×Q16—24no—
53C2×C11×SD16—22no—
54C2×C11×SD16—24no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#124—22no—
58C11×#124—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11D414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69Q8×Dic11—24no—
70Q8×Dic11—24no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4D412yes—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2312yes—
82#66941—216no—
83#66941—24no—
84#66941—24no—
85#66922—28no—
86#66922—22no—
87#66922D414yes—
88C4×Dic22—28no—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C11×C4⋊C8—22no—
92C11×#103—22no—
93C11×#102—22no—
94#66899—24no—
95#66899—24no—
96#66896—24no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100#66867—22no—
101#25942—111nomaximal, Sylow
102C24×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C2×D412yes—
110C2×Q8×C11#4114yes—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C2×Dic22—24no—
126C2×Dic22—28no—
127C2×Dic22—22no—
128C2×Dic22—24no—
129C2×Dic22—81no—
130C2×Dic22—81no—
131C2×Dic22—82no—
132C2×Dic22—82no—
133C11×Q16—44no—
134C11×SD16—44no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—42no—
144C42×C11—24no—
145C42×C11C2×D412yes—
146C42×C11C2×D412yes—
147C22⋊Dic11—44no—
148C22⋊Dic11—82no—
149C4⋊Dic11—28no—
150C4⋊Dic11—22no—
151C4⋊Dic11—24no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11C2×D414yes—
156Dic11⋊C4—28no—
157Dic11⋊C4—24no—
158C4×Dic11—28no—
159C4×Dic11—22no—
160C4×Dic11—22no—
161C4×Dic11—81no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×Q82—111no—
166C2×#489—111no—
167C2×#464D1111yescharacteristic
168#2592—111no—
169#2024—112no—
170#2023—112no—
171#1988—111no—
172#1985—111no—
173#1880—112no—
174#1878—112no—
175#1763—111no—
176C23×C11—41no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—22no—
183Q8×C11—24no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—42no—
187Q8×C11#12414yes—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—42no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11#12012yes—
202C2×C4×C11#12012yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4112yes—
206C2×C4×C112−1+412yes—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11#13714yes—
219Dic22—28no—
220Dic22—84no—
221Dic22—88no—
222C8×C11—41no—
223C8×C11—41no—
224C11⋊C8—42no—
225C22×Q16C2×D1111yescharacteristic
226C22×SD16C2×D1111yescharacteristic
227Q82—224no—
228Q82—224no—
229C2×C4⋊Q8—112no—
230C2×C4⋊Q8—111no—
231C2×C4⋊Q8—221no—
232C2×C4⋊Q8—222no—
233C2×#124C2×D1111yescharacteristic
234C2×C4×Q8—111no—
235C2×C4×Q8—112no—
236C2×C4×Q8—221no—
237C2×C4×Q8C2×D1111yescharacteristic
238#489—224no—
239#464—24no—
240C2×C4⋊C8C2×D1111yescharacteristic
241C2×#103—112no—
242C2×#103—112no—
243C2×#103C2×D1111yescharacteristic
244C2×#102—112no—
245C2×#102C2×D1111yescharacteristic
246C2×#97—111no—
247#397—221no—
248#393—221no—
249#391—112no—
250#390—112no—
251#388—222no—
252C4×C4⋊C4—111no—
253#340—112no—
254#340—112no—
255#340—112no—
256#336—112no—
257#336—112no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11C2×#12011yescharacteristic
264C22×C11#54812yes—
265C22×C11C2×#13712yes—
266C22×C11#57611yescharacteristic
267C22×C11#57711yescharacteristic
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—81no—
273C4×C11C2×#12411yescharacteristic
274C4×C11#53611yescharacteristic
275C4×C11#54812yes—
276Dic11—24no—
277Dic11—42no—
278Dic11—44no—
279Dic11—82no—
280C22×Q8—111no—
281C22×Q8—222no—
282C22×Q8—221no—
283C22×Q8C22×D1111yescharacteristic
284C22×Q8C22×D1111yescharacteristic
285C22×D4C22×D1111yescharacteristic
286C2×Q16—24no—
287C2×Q16—22no—
288C2×SD16—24no—
289C2×SD16—22no—
290C22×C8—112no—
291C22×C8C22×D1111yescharacteristic
292C22×C8C22×D1111yescharacteristic
293C4⋊Q8—114no—
294C4⋊Q8—228no—
295C4⋊Q8—224no—
296C4⋊Q8—2216no—
297C4⋊Q8—224no—
298C4⋊Q8—222no—
299#124—22no—
300#124—22no—
301C4×Q8—22no—
302C4×Q8—228no—
303C4×Q8—224no—
304C4×Q8—224no—
305C4×Q8—222no—
306C4×Q8—222no—
307C4×Q8C22⋊D1114yes—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—21no—
322C2×C42—112no—
323C2×C42—222no—
324C2×C42—221no—
325C2×C42C22×D1111yescharacteristic
326C4⋊C8—22no—
327#103—22no—
328#103—224no—
329#103—224no—
330#102—22no—
331#102—224no—
332#97—222no—
333#95—222no—
334#95—222no—
335#95—221no—
336C2×C11—161no—
337C2×C11#243611yescharacteristic
338C2×C11#300411yescharacteristic
339C2×C11#301211yescharacteristic
340C2×C11#336912yes—
341C2×C11#337512yes—
342C24—21no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—224no—
350C2×Q8—228no—
351C2×Q8—222no—
352C2×Q8—224no—
353C2×Q8—881no—
354C2×Q8—881no—
355C2×Q8—882no—
356C2×Q8—882no—
357C2×Q8#434114yes—
358C2×Q8C2×C22⋊D1112yes—
359C2×D4—21no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—112no—
367C22×C4—112no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372C22×C4C23×D1111yescharacteristic
373Q16—44no—
374SD16—44no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—222no—
382C4⋊C4—24no—
383C4⋊C4—21no—
384C4⋊C4—114no—
385C4⋊C4—228no—
386C4⋊C4—228no—
387C4⋊C4—224no—
388C4⋊C4—222no—
389C4⋊C4—224no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4C2×C22⋊D1112yes—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—444no—
397C22⋊C4—882no—
398C42—24no—
399C42—228no—
400C42—222no—
401C42—222no—
402C42—881no—
403C42D4×D1112yes—
404C42C2×C22⋊D1112yes—
405C11#2594211yescharacteristic, complemented, Sylow
406C23—41no—
407C23—41no—
408C23—42no—
409C23—41no—
410C23—42no—
411C23C2×D4×D1111yescharacteristic
412Q8—22no—
413Q8—24no—
414Q8—41no—
415Q8—41no—
416Q8—42no—
417Q8—228no—
418Q8—884no—
419Q8—888no—
420Q8#6698914yes—
421D4—41no—
422D4—41no—
423D4—42no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—114no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—224no—
440C2×C4—222no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4#6699012yes—
447C2×C4#6699012yes—
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4C2×#434112yes—
450C2×C4#6704312yes—
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—41no—
453C8—41no—
454C8—442no—
455C22—82no—
456C22—82no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22#1062312912yes—
461C22#1062330011yescharacteristic
462C22#1062330111yescharacteristic
463C22D11×#13712yes—
464C22C2×#6699011yescharacteristic
465C4—22no—
466C4—24no—
467C4—22no—
468C4—42no—
469C4—81no—
470C4—224no—
471C4—442no—
472C4—444no—
473C4—882no—
474C4#1062312912yes—
475C4C2×#6698911yescharacteristic
476C4#1062335611yescharacteristic
477C2—161no—
478C2#1307227511yescharacteristic
479C2#1307784811yescharacteristic
480C2#1307791611yescharacteristic
481C2#1308135112yes—
482C2#1308142512yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#464D11
hypocenterC11#25942
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic22C2semidirect
4. #13069755C2semidirect
6. #13069567C2semidirect
7. #13069555C2semidirect
9. #13068959C2semidirect
10. #13068446C2semidirect
405. C11#25942semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
C2×#106226682
#130741052
#130697552
#130697502
#130695672
#130695552
#130689732
#130689592
#130684462
C2×C11×#4642
#2594211