Finite Group Databasebeta

← #14908934

Subgroups — #14908934

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079259C211yesmaximal, characteristic, complemented
2#13077468C211yesmaximal, characteristic, complemented
3#13070808C211yesmaximal, characteristic, complemented
4#13070804C211yesmaximal, characteristic, complemented
5#13070775C211yesmaximal, characteristic, complemented
6#13070771C211yesmaximal, characteristic, complemented
7#13070649C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070528C211yesmaximal, characteristic, complemented
10#13070492C211yesmaximal, characteristic, complemented
11#13070489C211yesmaximal, characteristic, complemented
12D16×Dic11C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2184C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17#10623329—21no—
18#10623150—21no—
19C2×C11×D16C2211yescharacteristic
20C2×C11×D16C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622828—21no—
23#10622765—21no—
24#10622765—21no—
25#10622764C2211yescharacteristic, complemented
26D8×Dic11C2211yescharacteristic
27D8×Dic11C2211yescharacteristic
28D8×Dic11C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30D8×Dic11C2211yescharacteristic, complemented
31C2×#66890C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622719C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622652—21no—
37#10622491C2211yescharacteristic, complemented
38#10622485C2211yescharacteristic, complemented
39#10622398—21no—
40#10622377—21no—
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic, complemented
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×D8—22no—
61C2×C11×D8—22no—
62C2×C11×D8—21no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—21no—
68C2×C22⋊Dic11—41no—
69C2×C22⋊Dic11—41no—
70#66993—21no—
71#66992—41no—
72#66991—41no—
73D4×Dic11—21no—
74D4×Dic11—21no—
75D4×Dic11—21no—
76D4×Dic11—21no—
77D4×Dic11—21no—
78D4×Dic11—41no—
79D4×Dic11—41no—
80C2×#4323—21no—
81#66983—21no—
82#66979—21no—
83#66979D411yescharacteristic
84C2×#4318D411yescharacteristic
85C2×D88C2311yescharacteristic
86#66946—21no—
87#66943—21no—
88#66939—41no—
89#66936—41no—
90C11×D16—22no—
91C11×D16—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96#66896—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#66872—21no—
116#33682—111nomaximal, Sylow
117C24×C11—41no—
118C2×D4×C11—24no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—42no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C11×D8—24no—
137C11×D8—21no—
138C11×D8—21no—
139C11×D8—21no—
140C11×D8—21no—
141C11×D8#4112yes—
142C11×D8#4112yes—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C22⋊C4—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155C22⋊Dic11D811yescharacteristic
156C22⋊Dic11D811yescharacteristic
157#4323—42no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164C4⋊Dic11D811yescharacteristic
165C4⋊Dic11D811yescharacteristic
166Dic11⋊C4—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#3176—111no—
180#2948—111no—
181#2234—111no—
182#2234—111no—
183#2228—111no—
184#2228—111no—
185#2206—111no—
186#2206—111no—
187#2184—111no—
188#2184D1111yescharacteristic, complemented
189#2177—111no—
190#2177—111no—
191C4×D16—111no—
192C4×D16—111no—
193#2164—111no—
194C23×C11—44no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—161no—
199C23×C11—161no—
200C23×C11C2×D811yescharacteristic
201C22×D11—41no—
202D4×C11—22no—
203D4×C11—22no—
204D4×C11—44no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—161no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—161no—
216C22⋊D11—161no—
217C22⋊D11—161no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—161no—
222C2×Dic11—161no—
223C2×Dic11—161no—
224C2×Dic11—161no—
225C2×Dic11—161no—
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228C2×Dic11C2×D811yescharacteristic
229C2×Dic11C2×D811yescharacteristic
230D44—41no—
231D44—41no—
232C4×D11—161no—
233C8×C11—21no—
234C8×C11C2×#4111yescharacteristic
235C8×C11C2×#4111yescharacteristic
236C11⋊C8—21no—
237C11⋊C8—21no—
238C22×D8C2×D1111yescharacteristic
239#540—221no—
240#518—221no—
241C2×D16—111no—
242C2×D16—111no—
243C2×D16C2×D1111yescharacteristic
244C2×D16C2×D1111yescharacteristic
245#499—111no—
246#493—111no—
247#490—221no—
248#469—221no—
249#466—111no—
250#466C2×D1111yescharacteristic
251#442—221no—
252#442—221no—
253#442—221no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—111no—
257C4×D8—111no—
258C4×D8—111no—
259C4×D8—111no—
260#427—111no—
261#418—221no—
262#405—111no—
263#367—111no—
264#367—111no—
265#366—111no—
266#366—111no—
267C4⋊C16—111no—
268C4⋊C16—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357—111no—
273#357—111no—
274#357—111no—
275#357C2×D1111yescharacteristic
276#357C2×D1111yescharacteristic
277C22⋊C16—111no—
278C22⋊C16C2×D1111yescharacteristic
279#346—111no—
280C4×C16—111no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—164no—
294C22×C11C22×D811yescharacteristic
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C4×C11—21no—
299C4×C11—81no—
300C4×C11#52511yescharacteristic
301C4×C11#57511yescharacteristic
302Dic11—21no—
303Dic11—21no—
304Dic11—21no—
305Dic11—21no—
306Dic11—81no—
307Dic11—81no—
308Dic11—81no—
309C22×D4—21no—
310C2×D8—22no—
311C2×D8—22no—
312C2×D8—21no—
313C2×D8—111no—
314C2×D8—221no—
315C2×D8C22×D1111yescharacteristic
316C2×D8C22×D1111yescharacteristic
317C2×D8C22×D1111yescharacteristic
318C2×M16—111no—
319C22×C8C22×D1111yescharacteristic
320#127—221no—
321#125—221no—
322#123—441no—
323#123—441no—
324#121—21no—
325#121—221no—
326#121—441no—
327#121—441no—
328C4×D4—221no—
329C4×D4—221no—
330C4×D4—221no—
331C4×D4—221no—
332C4×D4—221no—
333C4×D4—221no—
334C4×D4—441no—
335C4×D4—441no—
336#117—111no—
337#117—221no—
338C2×C22⋊C4—441no—
339C2×C22⋊C4—441no—
340D16—22no—
341D16—22no—
342D16—222no—
343D16—222no—
344C2×C16—111no—
345C2×C16—111no—
346C2×C16C22×D1111yescharacteristic
347C2×C16C22×D1111yescharacteristic
348#107—111no—
349#107—111no—
350#107—111no—
351#107C22×D1111yescharacteristic
352#106—221no—
353#106—221no—
354#102—21no—
355#102—221no—
356#102—221no—
357#102—221no—
358#102—221no—
359#102—221no—
360#102—221no—
361#102—221no—
362#97—111no—
363#97—111no—
364C4×C8—111no—
365C4×C8—111no—
366C2×C11—41no—
367C2×C11—82no—
368C2×C11—82no—
369C2×C11—161no—
370C2×C11#310011yescharacteristic
371C2×C11#341511yescharacteristic
372C2×C11#341511yescharacteristic
373D11—161no—
374C24—41no—
375C2×D4—24no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—42no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—221no—
383C2×D4—441no—
384C2×D4—441no—
385C2×D4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4D4×D1111yescharacteristic
393D8—24no—
394D8—21no—
395D8—21no—
396D8—21no—
397D8—21no—
398D8—221no—
399D8—221no—
400D8—442no—
401D8#434112yes—
402D8#434112yes—
403M16—441no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—111no—
407C2×C8—111no—
408C2×C8D4×D1111yescharacteristic
409C2×C8C23×D1111yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—111no—
412C4⋊C4—111no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C22⋊C4—41no—
419C22⋊C4—111no—
420C22⋊C4—111no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C42—111no—
430C42—111no—
431C42—441no—
432C16—21no—
433C16—21no—
434C16—221no—
435C16—221no—
436C11#3368211yescharacteristic, complemented, Sylow
437C23—44no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—161no—
442C23—161no—
443C23—441no—
444C23D8×D1111yescharacteristic
445D4—22no—
446D4—22no—
447D4—44no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—161no—
453D4—441no—
454D4—441no—
455D4—1761no—
456D4—1761no—
457D4—1761no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—41no—
461C2×C4—111no—
462C2×C4—111no—
463C2×C4—111no—
464C2×C4—111no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—1761no—
469C2×C4—1761no—
470C2×C4—1761no—
471C2×C4—1761no—
472C2×C4—1761no—
473C2×C4—1761no—
474C2×C4D8×D1111yescharacteristic
475C2×C4C2×D4×D1111yescharacteristic
476C8—21no—
477C8—221no—
478C8—221no—
479C8C2×#434111yescharacteristic
480C8C2×#434111yescharacteristic
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—164no—
494C22—881no—
495C22—881no—
496C22—881no—
497C22C2×D8×D1111yescharacteristic
498C4—21no—
499C4—81no—
500C4—221no—
501C4—221no—
502C4—221no—
503C4—221no—
504C4—881no—
505C4—881no—
506C4—881no—
507C4#1062311711yescharacteristic
508C4#1062330411yescharacteristic
509C2—41no—
510C2—82no—
511C2—82no—
512C2—161no—
513C2—1761no—
514C2#1307861111yescharacteristic
515C2#1308175311yescharacteristic
516C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2184C2
socleC22×C11C22×D8
hypercenter#2184D11
hypocenterC11#33682
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #13079259C2semidirect
2. #13077468C2semidirect
3. #13070808C2semidirect
4. #13070804C2semidirect
5. #13070775C2semidirect
6. #13070771C2semidirect
7. #13070649C2semidirect
8. #13070649C2semidirect
9. #13070528C2semidirect
10. #13070492C2semidirect
11. #13070489C2semidirect
12. D16×Dic11C2semidirect
13. #13070460C2semidirect
14. #13070420C2semidirect
15. C11×#2184C2semidirect
25. #10622764C22semidirect
30. D8×Dic11C22semidirect
37. #10622491C22semidirect
38. #10622485C22semidirect
46. #10622200C22semidirect
47. #10622200C22semidirect
49. #10622147C22semidirect
50. #10622147C22semidirect
51. #10622143C22semidirect
52. #10622142C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
55. Dic11⋊C16C22semidirect
56. C16×Dic11C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
188. #2184D11semidirect
436. C11#33682semidirect

Maximal subgroups

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

subgroupindex
#130792592
#130774682
#130708082
#130708042
#130707752
#130707712
#130706492
#130705282
#130704922
#130704892
D16×Dic112
#130704602
#130704202
C11×#21842
#3368211