Finite Group Databasebeta

← #14910261

Subgroups — #14910261

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622528C211yesmaximal, characteristic, complemented
2Q16×C22⋊D11C211yesmaximal, characteristic, complemented
3#13080301C211yesmaximal, characteristic
4#13070886C211yesmaximal, characteristic, complemented
5#13070726C211yesmaximal, characteristic, complemented
6#13070707C211yesmaximal, characteristic, complemented
7#13070676C211yesmaximal, characteristic, complemented
8#13070659C211yesmaximal, characteristic, complemented
9#13070553C211yesmaximal, characteristic, complemented
10#13070550C211yesmaximal, characteristic, complemented
11#13070545C211yesmaximal, characteristic, complemented
12#13070531C211yesmaximal, characteristic, complemented
13#13070481C211yesmaximal, characteristic, complemented
14#13070441C211yesmaximal, characteristic, complemented
15C22×C11×SD32C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18Q8×C22⋊D11—21no—
19#10623337—21no—
20C2×Q16×D11C2211yescharacteristic, complemented
21C2×#66965C2211yescharacteristic
22C2×C11×SD32—24no—
23C2×C11×SD32C2211yescharacteristic
24C2×C11×SD32C2211yescharacteristic
25C2×C11×SD32C2211yescharacteristic
26C2×C11×SD32C2211yescharacteristic
27C22×C11×C16C2211yescharacteristic
28#10622841—21no—
29#10622831—21no—
30#10622801C2211yescharacteristic, complemented
31#10622799—21no—
32Q16×Dic11C2211yescharacteristic, complemented
33#10622795—21no—
34#10622794C2211yescharacteristic, complemented
35C2×#66893C2211yescharacteristic, complemented
36C2×#66893C2211yescharacteristic, complemented
37#10622771—21no—
38#10622770C2211yescharacteristic
39#10622768C2211yescharacteristic
40#10622766—21no—
41D8×Dic11C2211yescharacteristic
42C2×#66891C2211yescharacteristic
43C2×#66891C2211yescharacteristic
44#10622729C2211yescharacteristic
45#10622729C2211yescharacteristic
46C8×C22⋊D11C2211yescharacteristic
47#10622528—24no—
48C2×Dic88C2211yescharacteristic, complemented
49C2×#66862C2211yescharacteristic, complemented
50#10622202C2211yescharacteristic, complemented
51#10622202C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic
53#10622200C2211yescharacteristic
54C22⋊(C11⋊C16)C2211yescharacteristic
55(C2×D11)⋊C16C2211yescharacteristic, complemented
56#10622142C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59#10622140C2211yescharacteristic, complemented
60Dic11⋊C16C2211yescharacteristic, complemented
61C22×Q8×C11—21no—
62C22×D4×C11—21no—
63C2×Q8×D11—21no—
64C2×#4341—21no—
65C2×C11×Q16—22no—
66C2×C11×Q16—21no—
67C2×C11×Q16—41no—
68C2×C11×Q16C2311yescharacteristic
69C2×C11×Q16C2311yescharacteristic
70C2×C11×D8—22no—
71C2×C11×D8—21no—
72C2×C11×D8—41no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76#67006—41no—
77C2×C22⋊Dic11—41no—
78#66999—21no—
79#66999—41no—
80Q8×Dic11—21no—
81#66997—21no—
82#66997—41no—
83C2×#4326—21no—
84C2×#4326—21no—
85#66992—41no—
86#66991—21no—
87#66989—21no—
88#66988—41no—
89D4×Dic11—21no—
90C2×#4324—21no—
91C2×#4324—21no—
92C4×C22⋊D11—41no—
93C4×C22⋊D11D411yescharacteristic
94#66977—21no—
95#66977—21no—
96#66977—41no—
97Q16×D11—22no—
98Q16×D11—41no—
99#66965—22no—
100#66965—41no—
101C2×Dic44C2311yescharacteristic
102C2×Dic44C2311yescharacteristic
103C2×C8×D11C2311yescharacteristic
104C11×SD32—22no—
105C11×SD32—22no—
106C11×SD32—22no—
107C11×SD32D414yescomplemented
108C2×C11×C16—22no—
109C2×C11×C16C2311yescharacteristic
110C2×C11×C16C2311yescharacteristic
111#66899—21no—
112#66899—21no—
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116#66893—22no—
117#66893—41no—
118#66891—22no—
119#66891—41no—
120(C2×D11)⋊C8D411yescharacteristic
121#66882C2311yescharacteristic
122#66882C2311yescharacteristic
123#66880—21no—
124#66880—21no—
125Dic11⋊C8D411yescharacteristic
126C8×Dic11C2311yescharacteristic
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129Dic88—22no—
130#66862—22no—
131#33832—111nomaximal, Sylow
132C24×C11—41no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—42no—
136C2×Q8×C11—41no—
137C2×Q8×C11—81no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—42no—
141C2×D4×C11—41no—
142C2×D4×C11—81no—
143C22×C4×C11—41no—
144C22×C4×C11C2×D411yescharacteristic
145C2×C22⋊D11—41no—
146C2×C22⋊D11—41no—
147C2×C22⋊D11D811yescharacteristic
148C22×Dic11—41no—
149C22×Dic11—41no—
150Q8×D11—42no—
151Q8×D11—81no—
152#4341—42no—
153#4341—81no—
154C2×C4×D11—41no—
155C2×C4×D11C2×D411yescharacteristic
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—41no—
159C11×Q16—21no—
160C11×Q16—21no—
161C11×Q16—21no—
162C11×Q16—42no—
163C11×Q16C2×D412yes—
164C11×D8—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—42no—
168C11×D8C2×D412yes—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2411yescharacteristic
173C22⋊Dic11—41no—
174C22⋊Dic11—41no—
175C22⋊Dic11—41no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179C22⋊Dic11D811yescharacteristic
180#4326—42no—
181#4326—81no—
182#4324—42no—
183#4324—81no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4D811yescharacteristic
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—41no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194Dic11⋊C4D811yescharacteristic
195C4×Dic11—41no—
196C4×Dic11C2×D411yescharacteristic
197C2×C11⋊C8C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199Dic44—21no—
200Dic44—21no—
201Dic44—21no—
202Dic44—21no—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16C2×D412yes—
207C11⋊C16—21no—
208C11⋊C16—21no—
209C2×#510—111no—
210C22×SD32D1111yescharacteristic, complemented
211D4×Q16—111no—
212#3280—111no—
213#2251—111no—
214#2220—111no—
215#2216—111no—
216#2211—111no—
217#2208—111no—
218#2189—111no—
219#2188—111no—
220#2187—111no—
221#2185—111no—
222#2175—111no—
223#2168—111no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—82no—
227C23×C11—82no—
228C23×C11—161no—
229C23×C11C2×D811yescharacteristic
230C22×D11C2×D811yescharacteristic
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—82no—
236D4×C11—22no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—82no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—82no—
246C2×C4×C11C2×D811yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C22⋊D11—22no—
249C22⋊D11—82no—
250C22⋊D11—161no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—82no—
256C2×Dic11—161no—
257C2×Dic11C2×D811yescharacteristic
258C2×Dic11C2×D811yescharacteristic
259C2×Dic11C2×D811yescharacteristic
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—82no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—82no—
268C8×C11—21no—
269C8×C11C22×D411yescharacteristic
270C8×C11H(5,𝔽2)11yescharacteristic
271C11⋊C8—21no—
272C11⋊C8—21no—
273C2×#135—111no—
274C22×Q16—111no—
275C22×Q16C2×D1111yescharacteristic
276C22×D8C2×D1111yescharacteristic
277D4×Q8—221no—
278#546—221no—
279#510—224no—
280C2×Q32—111no—
281C2×Q32—111no—
282C2×Q32—111no—
283C2×SD32—24no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32C2×D1111yescharacteristic
287C2×SD32C2×D1111yescharacteristic
288C2×SD32C2×D1111yescharacteristic
289C2×SD32C2×D1111yescharacteristic
290C2×M32—111no—
291C22×C16C2×D1111yescharacteristic
292#495—111no—
293#494—111no—
294#467—111no—
295#467—111no—
296#467—111no—
297#466—111no—
298#463—221no—
299#462—221no—
300#451—221no—
301#451—221no—
302#450—221no—
303#449—221no—
304C4×Q16—111no—
305C4×D8—111no—
306C8×D4—111no—
307#366—111no—
308C4⋊C16—111no—
309#358—111no—
310#358—111no—
311#358—111no—
312#358—111no—
313#357—111no—
314#357—111no—
315C22⋊C16—111no—
316C22⋊C16—111no—
317#346—111no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—42no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—164no—
327C22×C11#51012yescomplemented
328C22×C11C22×D811yescharacteristic
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C4×C11—21no—
333C4×C11—42no—
334C4×C11—81no—
335C4×C11D4211yescharacteristic
336C4×C11#57611yescharacteristic
337Dic11—21no—
338Dic11—21no—
339Dic11—21no—
340Dic11—81no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344C2×#41—221no—
345C22×Q8—21no—
346C22×Q8—221no—
347C22×D4—21no—
348#135—222no—
349#135—441no—
350C2×Q16—22no—
351C2×Q16—21no—
352C2×Q16—41no—
353C2×Q16—111no—
354C2×Q16—111no—
355C2×Q16—221no—
356C2×Q16—221no—
357C2×Q16—222no—
358C2×Q16—441no—
359C2×Q16C22×D1111yescharacteristic
360C2×Q16C22×D1111yescharacteristic
361C2×SD16—221no—
362C2×SD16—221no—
363C2×D8—22no—
364C2×D8—21no—
365C2×D8—41no—
366C2×D8C22×D1111yescharacteristic
367C2×D8C22×D1111yescharacteristic
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C4⋊Q8—221no—
371C4⋊Q8—441no—
372#124—221no—
373#123—441no—
374C22⋊Q8—221no—
375C22⋊Q8—221no—
376C22⋊Q8—221no—
377C22⋊Q8—441no—
378C22⋊Q8—441no—
379#121—221no—
380#121—441no—
381#120—441no—
382C4×Q8—221no—
383C4×D4—111no—
384C4×D4—221no—
385C4×D4—441no—
386C2×C22⋊C4—441no—
387Q32—222no—
388Q32—222no—
389Q32—441no—
390SD32—22no—
391SD32—22no—
392SD32—22no—
393SD32—222no—
394SD32—441no—
395SD32C22⋊D1114yescomplemented
396M32—222no—
397C2×C16—22no—
398C2×C16—111no—
399C2×C16—111no—
400C2×C16C22×D1111yescharacteristic
401C2×C16C22×D1111yescharacteristic
402#107—111no—
403#107—111no—
404C4⋊C8—111no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#102—221no—
410#102—221no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C4×C8—111no—
414C2×C11—22no—
415C2×C11—82no—
416C2×C11—161no—
417C2×C11D4×D811yescharacteristic
418C2×C11C2×#51011yescharacteristic
419C2×C11#341611yescharacteristic
420D11—41no—
421C24—41no—
422#41—442no—
423#41—881no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—42no—
427C2×Q8—41no—
428C2×Q8—81no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—441no—
432C2×Q8—442no—
433C2×Q8—881no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—81no—
439C2×D4—111no—
440C2×D4—441no—
441C2×D4—441no—
442C22×C4—41no—
443C22×C4—111no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4D4×D1111yescharacteristic
448Q16—21no—
449Q16—21no—
450Q16—21no—
451Q16—42no—
452Q16—221no—
453Q16—221no—
454Q16—221no—
455Q16—221no—
456Q16—442no—
457Q16—881no—
458Q16C2×C22⋊D1112yes—
459SD16—442no—
460SD16—881no—
461D8—21no—
462D8—21no—
463D8—21no—
464D8—42no—
465D8C2×C22⋊D1112yes—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8D4×D1111yescharacteristic
473C2×C8C23×D1111yescharacteristic
474C4⋊C4—111no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C22⋊C4—111no—
484C22⋊C4—111no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C42—111no—
493C42—441no—
494C16—21no—
495C16—221no—
496C16—221no—
497C16C2×C22⋊D1112yes—
498C11#3383211yescharacteristic, complemented, Sylow
499C23—41no—
500C23—41no—
501C23—82no—
502C23—82no—
503C23—111no—
504C23—161no—
505C23D8×D1111yescharacteristic
506Q8—22no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—82no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515Q8—882no—
516D4—22no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—82no—
521D4—222no—
522D4—882no—
523D4—1761no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—111no—
530C2×C4—111no—
531C2×C4—111no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—882no—
539C2×C4—882no—
540C2×C4—1761no—
541C2×C4D8×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C8—21no—
544C8—221no—
545C8—221no—
546C8#6703711yescharacteristic
547C8C22×C22⋊D1111yescharacteristic
548C22—21no—
549C22—21no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—164no—
557C22—221no—
558C22—221no—
559C22—221no—
560C22#1062252812yescomplemented
561C22C2×D8×D1111yescharacteristic
562C4—21no—
563C4—42no—
564C4—81no—
565C4—221no—
566C4—221no—
567C4—221no—
568C4—881no—
569C4—881no—
570C4—881no—
571C4—881no—
572C4#1062328811yescharacteristic
573C4D4×C22⋊D1111yescharacteristic
574C2—22no—
575C2—82no—
576C2—161no—
577C2—441no—
578C2D8×C22⋊D1111yescharacteristic
579C2C2×#1062252811yescharacteristic
580C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×SD32C2
socleC22×C11C22×D8
prime radical#13080301C2
hypercenterC22×SD32D11
hypocenterC11#33832
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#10622528C2semidirect
2. Q16×C22⋊D11C2semidirect
4. #13070886C2semidirect
5. #13070726C2semidirect
6. #13070707C2semidirect
7. #13070676C2semidirect
8. #13070659C2semidirect
9. #13070553C2semidirect
10. #13070550C2semidirect
11. #13070545C2semidirect
12. #13070531C2semidirect
13. #13070481C2semidirect
14. #13070441C2semidirect
15. C22×C11×SD32C2semidirect
20. C2×Q16×D11C22semidirect
30. #10622801C22semidirect
32. Q16×Dic11C22semidirect
34. #10622794C22semidirect
35. C2×#66893C22semidirect
36. C2×#66893C22semidirect
48. C2×Dic88C22semidirect
49. C2×#66862C22semidirect
50. #10622202C22semidirect
51. #10622202C22semidirect
55. (C2×D11)⋊C16C22semidirect
56. #10622142C22semidirect
57. #10622141C22semidirect
58. #10622141C22semidirect
59. #10622140C22semidirect
60. Dic11⋊C16C22semidirect
107. C11×SD32D4semidirect
210. C22×SD32D11semidirect
327. C22×C11#510semidirect
395. SD32C22⋊D11semidirect
498. C11#33832semidirect
560. C22#10622528semidirect

Maximal subgroups

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

subgroupindex
C2×#106225282
Q16×C22⋊D112
#130803012
#130708862
#130707262
#130707072
#130706762
#130706592
#130705532
#130705502
#130705452
#130705312
#130704812
#130704412
C22×C11×SD322
#3383211