Finite Group Databasebeta

← #14908882

Subgroups — #14908882

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079256C211yesmaximal, characteristic, complemented
2#13077468C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic, complemented
5#13070761C211yesmaximal, characteristic, complemented
6#13070751C211yesmaximal, characteristic, complemented
7#13070673C211yesmaximal, characteristic, complemented
8#13070673C211yesmaximal, characteristic, complemented
9#13070528C211yesmaximal, characteristic
10#13070489C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12SD32×Dic11C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2187C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17#10623329—21no—
18#10623174—21no—
19C2×C11×SD32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C11×#467C2211yescharacteristic
22#10622828—21no—
23#10622804C2211yescharacteristic, complemented
24Q16×Dic11C2211yescharacteristic, complemented
25#10622765—21no—
26#10622765—21no—
27D8×Dic11C2211yescharacteristic
28D8×Dic11C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622719C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622662—21no—
37#10622487C2211yescharacteristic, complemented
38#10622485C2211yescharacteristic, complemented
39#10622430—21no—
40#10622408—21no—
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic, complemented
50#10622147C2211yescharacteristic, complemented
51#10622143C2211yescharacteristic, complemented
52#10622142C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54Dic11⋊C16C2211yescharacteristic, complemented
55Dic11⋊C16C2211yescharacteristic, complemented
56C16×Dic11C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×D8—22no—
62C2×C11×D8—22no—
63C2×C11×D8—21no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—21no—
68C2×C22⋊Dic11—41no—
69C2×C22⋊Dic11—41no—
70#67000—21no—
71Q8×Dic11—21no—
72C2×#4325—21no—
73D4×Dic11—21no—
74D4×Dic11—21no—
75D4×Dic11—21no—
76D4×Dic11—21no—
77D4×Dic11—41no—
78D4×Dic11—41no—
79#66983—21no—
80#66979—21no—
81#66979D411yescharacteristic
82C2×#4318D411yescharacteristic
83C2×D88C2311yescharacteristic
84#66951—41no—
85#66950—41no—
86#66946—21no—
87#66941—21no—
88#66938—41no—
89#66936—41no—
90C11×SD32—22no—
91C11×SD32—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96#66899—21no—
97#66896—21no—
98#66896—21no—
99#66896—21no—
100#66896—21no—
101#66890—22no—
102#66890—22no—
103#66885—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66879D411yescharacteristic
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66873—21no—
115#66871—21no—
116#33678—111nomaximal, Sylow
117C24×C11—41no—
118C2×Q8×C11—21no—
119C2×D4×C11—24no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—42no—
123C2×D4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129C22×Dic11—41no—
130C2×D44—21no—
131C2×C4×D11—41no—
132C2×Dic22—41no—
133C11×Q16—21no—
134C11×Q16—21no—
135C11×D8—24no—
136C11×D8—21no—
137C11×D8—21no—
138C11×D8#4112yes—
139C11×D8#4112yes—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2411yescharacteristic
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11D811yescharacteristic
153C22⋊Dic11D811yescharacteristic
154#4325—42no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—41no—
163C4⋊Dic11D811yescharacteristic
164C4⋊Dic11D811yescharacteristic
165Dic11⋊C4—41no—
166C4×Dic11—41no—
167C4×Dic11—41no—
168C4×Dic11C2×D411yescharacteristic
169C4×Dic11C2×D411yescharacteristic
170#4318—41no—
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173D88—21no—
174D88—21no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3175—111no—
180#2948—111no—
181#2237—111no—
182#2234—111no—
183#2226—111no—
184#2224—111no—
185#2210—111no—
186#2210—111no—
187#2187D1111yescharacteristic, complemented
188#2184—111no—
189#2177—111no—
190#2175—111no—
191C4×SD32—111no—
192C4×D16—111no—
193#2164—111no—
194C23×C11—44no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—161no—
198C23×C11—161no—
199C23×C11C2×D811yescharacteristic
200C22×D11—41no—
201Q8×C11—41no—
202Q8×C11—41no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—44no—
206D4×C11—41no—
207D4×C11—41no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—161no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—161no—
219C2×Dic11—161no—
220C2×Dic11—161no—
221C2×Dic11—161no—
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226D44—41no—
227D44—41no—
228C4×D11—161no—
229Dic22—161no—
230C8×C11—21no—
231C8×C11C2×#4111yescharacteristic
232C8×C11C2×#4111yescharacteristic
233C11⋊C8—21no—
234C11⋊C8—21no—
235C22×D8C2×D1111yescharacteristic
236#542—221no—
237#518—221no—
238C2×SD32C2×D1111yescharacteristic
239C2×SD32C2×D1111yescharacteristic
240C2×D16—111no—
241C2×D16—111no—
242#500—111no—
243#495—111no—
244#489—221no—
245#468—221no—
246#467C2×D1111yescharacteristic
247#466—111no—
248#442—221no—
249#442—221no—
250#440—221no—
251C4×Q16—111no—
252C4×D8—111no—
253C4×D8—111no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—111no—
257#427—111no—
258#418—221no—
259#405—111no—
260#367—111no—
261#367—111no—
262#366—111no—
263#366—111no—
264C4⋊C16—111no—
265C4⋊C16—111no—
266#358—111no—
267#358—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357C2×D1111yescharacteristic
273#357C2×D1111yescharacteristic
274C22⋊C16—111no—
275C22⋊C16C2×D1111yescharacteristic
276#346—111no—
277C4×C16—111no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—164no—
288C22×C11C22×D811yescharacteristic
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
292C4×C11—21no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11#52511yescharacteristic
296C4×C11#57511yescharacteristic
297Dic11—21no—
298Dic11—21no—
299Dic11—21no—
300Dic11—21no—
301Dic11—81no—
302Dic11—81no—
303Dic11—81no—
304C22×D4—21no—
305C2×Q16C22×D1111yescharacteristic
306C2×SD16—221no—
307C2×D8—22no—
308C2×D8—22no—
309C2×D8—21no—
310C2×D8—111no—
311C2×D8C22×D1111yescharacteristic
312C2×D8C22×D1111yescharacteristic
313C2×M16—111no—
314C22×C8C22×D1111yescharacteristic
315C4⋊Q8—221no—
316#126—441no—
317#124—221no—
318#124—441no—
319#123—441no—
320C22⋊Q8—21no—
321C22⋊Q8—441no—
322#121—221no—
323C4×Q8—221no—
324C4×D4—221no—
325C4×D4—221no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4—441no—
330C4×D4—441no—
331#117—111no—
332#117—221no—
333C2×C22⋊C4—441no—
334C2×C22⋊C4—441no—
335SD32—22no—
336SD32—22no—
337D16—222no—
338D16—222no—
339C2×C16—111no—
340C2×C16—111no—
341C2×C16C22×D1111yescharacteristic
342C2×C16C22×D1111yescharacteristic
343#107—111no—
344#107—111no—
345#107—111no—
346#107—221no—
347#107C22×D1111yescharacteristic
348#106—221no—
349#103—21no—
350#103—221no—
351#102—221no—
352#102—221no—
353#102—221no—
354#102—221no—
355#102—221no—
356#102—221no—
357#97—111no—
358#97—111no—
359C4×C8—111no—
360C4×C8—111no—
361C2×C11—41no—
362C2×C11—82no—
363C2×C11—82no—
364C2×C11#310011yescharacteristic
365C2×C11#341511yescharacteristic
366C2×C11#341611yescharacteristic
367D11—161no—
368C24—41no—
369C2×Q8—21no—
370C2×Q8—441no—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—42no—
375C2×D4—41no—
376C2×D4—221no—
377C2×D4—441no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4D4×D1111yescharacteristic
384Q16—21no—
385Q16—21no—
386SD16—442no—
387D8—24no—
388D8—21no—
389D8—21no—
390D8—221no—
391D8—221no—
392D8#434112yes—
393D8#434112yes—
394M16—441no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—111no—
398C2×C8—111no—
399C2×C8D4×D1111yescharacteristic
400C2×C8C23×D1111yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—111no—
404C4⋊C4—111no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—441no—
409C4⋊C4—441no—
410C22⋊C4—41no—
411C22⋊C4—111no—
412C22⋊C4—111no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C42—111no—
423C42—111no—
424C42—441no—
425C42—441no—
426C16—21no—
427C16—21no—
428C16—221no—
429C16—221no—
430C11#3367811yescharacteristic, complemented, Sylow
431C23—44no—
432C23—41no—
433C23—41no—
434C23—161no—
435C23—161no—
436C23—441no—
437C23D8×D1111yescharacteristic
438Q8—41no—
439Q8—41no—
440Q8—1761no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—441no—
447D4—441no—
448D4—1761no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—111no—
454C2×C4—111no—
455C2×C4—111no—
456C2×C4—111no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—1761no—
461C2×C4—1761no—
462C2×C4—1761no—
463C2×C4—1761no—
464C2×C4—1761no—
465C2×C4D8×D1111yescharacteristic
466C2×C4C2×D4×D1111yescharacteristic
467C8—21no—
468C8—221no—
469C8—221no—
470C8C2×#434111yescharacteristic
471C8C2×#434111yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—164no—
482C22—881no—
483C22—881no—
484C22—881no—
485C22C2×D8×D1111yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—221no—
490C4—221no—
491C4—221no—
492C4—221no—
493C4—881no—
494C4—881no—
495C4—881no—
496C4#1062311711yescharacteristic
497C4#1062330411yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—1761no—
502C2#1307861111yescharacteristic
503C2#1308175611yescharacteristic
504C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
prime radical#13070528C2
hypercenter#2187D11
hypocenterC11#33678
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #13079256C2semidirect
2. #13077468C2semidirect
3. #13070821C2semidirect
4. #13070808C2semidirect
5. #13070761C2semidirect
6. #13070751C2semidirect
7. #13070673C2semidirect
8. #13070673C2semidirect
10. #13070489C2semidirect
11. #13070481C2semidirect
12. SD32×Dic11C2semidirect
13. #13070460C2semidirect
14. #13070420C2semidirect
15. C11×#2187C2semidirect
23. #10622804C22semidirect
24. Q16×Dic11C22semidirect
37. #10622487C22semidirect
38. #10622485C22semidirect
44. #10622202C22semidirect
45. #10622202C22semidirect
49. #10622147C22semidirect
50. #10622147C22semidirect
51. #10622143C22semidirect
52. #10622142C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
55. Dic11⋊C16C22semidirect
56. C16×Dic11C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
187. #2187D11semidirect
430. C11#33678semidirect

Maximal subgroups

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

subgroupindex
#130792562
#130774682
#130708212
#130708082
#130707612
#130707512
#130706732
#130705282
#130704892
#130704812
SD32×Dic112
#130704602
#130704202
C11×#21872
#3367811