Finite Group Databasebeta

← #14726696

Subgroups — #14726696

Order 2816.

1370 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C212yesmaximal, complemented
2#13071972C211yesmaximal, characteristic
3#13067556C214yesmaximal, complemented
4#13067539C214yesmaximal, complemented
5#13067188C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic, complemented
7C11×#3501C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C11×#554—24no—
10C11×#554—22no—
11D4×Q8×C11—22no—
12C11×#544C2212yescomplemented
13C11×#543—21no—
14C11×#543C2212yescomplemented
15C11×#533—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8C2212yes—
18C11×#518—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4325—22no—
21C2×#66990—21no—
22C2×#66983—21no—
23#10622825C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2212yes—
25#10622659—24no—
26#10622659C2218yes—
27#10622604C2212yes—
28C2×#66873—22no—
29#10622573C2212yes—
30#10622568—21no—
31#10622552—21no—
32#10622176C2218yescomplemented
33#10622166C2212yescomplemented
34#10622163C2212yescomplemented
35C24×D11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11D412yescomplemented
38C22×D4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—22no—
42C22×D44—22no—
43C22×D44—21no—
44C22×D44—22no—
45C22×D44—44no—
46C22×D44C2312yes—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—24no—
50C11×#125—22no—
51C11×#125—24no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8D414yescomplemented
63C11×C22⋊Q8C2314yes—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4D412yescomplemented
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4C2311yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×#4325—28no—
83C2×#4325—48no—
84#66990—44no—
85#66983—44no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×C4⋊Dic11—21no—
90C22×C11⋊C8—22no—
91C11⋊#95C2312yes—
92C22⋊(C11⋊C8)—22no—
93C22⋊(C11⋊C8)C2314yes—
94#66873—28no—
95#18196—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C24×C11C2×D411yescharacteristic
98C23×D11—22no—
99C23×D11—44no—
100C23×D11—42no—
101C23×D11—42no—
102C23×D11—42no—
103C23×D11—82no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—44no—
108C2×Q8×C11—82no—
109C2×Q8×C11C2×D414yes—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11SD1614yescomplemented
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—44no—
129C2×C22⋊D11—44no—
130C2×C22⋊D11—82no—
131C22×Dic11—22no—
132C2×D44—24no—
133C2×D44—28no—
134C2×D44—24no—
135C2×D44—44no—
136C2×D44—42no—
137C2×D44—44no—
138C2×D44—48no—
139C2×D44—41no—
140C2×D44—41no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C2×D414yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—22no—
157C42×C11—24no—
158C42×C11—21no—
159C42×C11—21no—
160C22⋊Dic11—42no—
161#4325—416no—
162(C2×D11)⋊C4—44no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—82no—
165C4⋊Dic11—42no—
166C2×C11⋊C8—24no—
167C2×C11⋊C8—44no—
168#3501D1111yescharacteristic, complemented
169C2×#450—112no—
170#2408—111no—
171#1599—114no—
172#1596—114no—
173#1520—112no—
174#1459—111no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11#12012yes—
182C23×C11C2×SD1612yes—
183C23×C11C2×SD1612yescomplemented
184C23×C11#13712yes—
185C23×C11C22×D411yescharacteristic
186C22×D11—24no—
187C22×D11—42no—
188C22×D11—48no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—88no—
195C22×D11—88no—
196C22×D11—84no—
197C22×D11—84no—
198Q8×C11—44no—
199Q8×C11—44no—
200Q8×C11—82no—
201Q8×C11—82no—
202D4×C11—28no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—21no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—81no—
217C2×C4×C11—82no—
218C2×C4×C11—82no—
219C2×C4×C11—82no—
220C2×C4×C11—82no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11C2×SD1612yescomplemented
224C2×C4×C11C22×D412yes—
225C22⋊D11—88no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229D44—28no—
230D44—44no—
231D44—44no—
232D44—44no—
233C11⋊C8—44no—
234C23×D4—111no—
235C22×SD16—222no—
236#554—24no—
237#554—22no—
238D4×Q8—22no—
239#544C2×D1112yescomplemented
240#543—21no—
241#543C2×D1112yescomplemented
242#533—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2×D1112yes—
245C2×#121—221no—
246C2×#120—221no—
247#518—21no—
248C2×C4×D4C2×D1111yescharacteristic
249#450—118no—
250#450—224no—
251C2×#102—222no—
252C2×C22⋊C8—112no—
253#394—112no—
254#392—112no—
255#390—221no—
256#380—111no—
257#379—221no—
258#328—118no—
259#324—112no—
260#323—112no—
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—21no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—81no—
272C22×C11#44814yes—
273C22×C11C2×#12011yescharacteristic
274C22×C11C22×SD1611yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—44no—
279C2×D11—82no—
280C2×D11—82no—
281C2×D11—816no—
282C2×D11—82no—
283C2×D11—82no—
284C4×C11—22no—
285C4×C11—21no—
286C4×C11—22no—
287C4×C11—41no—
288C4×C11—44no—
289C4×C11—41no—
290C4×C11—44no—
291C4×C11B(4,𝔽2)12yes—
292Dic11—82no—
293C25—221no—
294C22×Q8—21no—
295C22×Q8C22⋊D1112yescomplemented
296C22×D4—112no—
297C22×D4—222no—
298C22×D4—222no—
299C22×D4—221no—
300C22×D4—222no—
301C22×D4—444no—
302C22×D4C22⋊D1111yescharacteristic
303C23×C4C22⋊D1111yescharacteristic
304C23×C4C22×D1111yescharacteristic
305C2×SD16—228no—
306C2×SD16—448no—
307C22×C8—222no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—24no—
311#125—22no—
312#125—24no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8C22⋊D1114yescomplemented
324C22⋊Q8C22×D1114yes—
325#121—444no—
326#120—444no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—22no—
332C4×D4—22no—
333#117—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4C22⋊D1112yescomplemented
339C2×C4⋊C4C22×D1111yescharacteristic
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—222no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C2×C22⋊C4C22⋊D1111yescharacteristic
347C2×C22⋊C4C22×D1111yescharacteristic
348C2×C42C22⋊D1111yescharacteristic
349#102—228no—
350C22⋊C8—114no—
351C22⋊C8—222no—
352#95—112no—
353C2×C11—21no—
354C2×C11—21no—
355C2×C11—24no—
356C2×C11—42no—
357C2×C11C2×#44811yescharacteristic
358C2×C11#302111yescharacteristic
359C2×C11C2×B(4,𝔽2)11yescharacteristic
360D11—84no—
361C24—222no—
362C24—444no—
363C24—442no—
364C24—442no—
365C24—442no—
366C24—882no—
367C24C2×C22⋊D1111yescharacteristic
368C24C2×C22⋊D1111yescharacteristic
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—44no—
373C2×Q8—82no—
374C2×Q8C2×C22⋊D1114yes—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—228no—
378C2×D4—224no—
379C2×D4—224no—
380C2×D4—442no—
381C2×D4—444no—
382C2×D4—444no—
383C2×D4—448no—
384C2×D4—444no—
385C2×D4—444no—
386C2×D4—441no—
387C2×D4—441no—
388C2×D4—882no—
389C2×D4#432514yescomplemented
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—222no—
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1112yes—
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1111yescharacteristic
404C22×C4C2×C22⋊D1112yes—
405C22×C4C23×D1111yescharacteristic
406SD16—4416no—
407C2×C8—224no—
408C2×C8—444no—
409C4⋊C4—22no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—24no—
414C4⋊C4—22no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—442no—
420C4⋊C4C2×C22⋊D1114yes—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4—444no—
427C22⋊C4—442no—
428C22⋊C4—444no—
429C22⋊C4—882no—
430C42—24no—
431C42—21no—
432C42—21no—
433C11#1819611yescharacteristic, complemented, Sylow
434C23—21no—
435C23—21no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—224no—
441C23—442no—
442C23—448no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23—442no—
447C23—442no—
448C23—884no—
449C23—888no—
450C23—888no—
451C23—884no—
452C23C2×#432512yes—
453C23C2×#432512yescomplemented
454C23#6699512yes—
455C23#6700612yes—
456C23C22×C22⋊D1111yescharacteristic
457Q8—44no—
458Q8—44no—
459Q8—82no—
460Q8—82no—
461D4—28no—
462D4—228no—
463D4—444no—
464D4—444no—
465D4—444no—
466D4—888no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—21no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—81no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4C2×#432512yescomplemented
489C2×C4#6700611yescharacteristic
490C2×C4#6700611yescharacteristic
491C2×C4C22×C22⋊D1112yes—
492C8—444no—
493C22—21no—
494C22—22no—
495C22—21no—
496C22—22no—
497C22—22no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—41no—
503C22—81no—
504C22—444no—
505C22—444no—
506C22—444no—
507C22—882no—
508C22—882no—
509C22—8816no—
510C22—882no—
511C22—882no—
512C22#1062284014yes—
513C22C22×#432511yescharacteristic
514C22C2×#6699511yescharacteristic
515C22C2×#6700611yescharacteristic
516C4—22no—
517C4—22no—
518C4—21no—
519C4—41no—
520C4—44no—
521C4—41no—
522C4—44no—
523C4—882no—
524C4#1062285712yes—
525C2—21no—
526C2—21no—
527C2—24no—
528C2—42no—
529C2—884no—
530C2C2×#1062284011yescharacteristic
531C2#1307798811yescharacteristic
532C2C2×#1062285711yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radical#13071972C2
hypercenter#3501D11
hypocenterC11#18196
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. C2×#10622659C2semidirect
3. #13067556C2semidirect
4. #13067539C2semidirect
5. #13067188C2semidirect
6. #13066934C2semidirect
7. C11×#3501C2semidirect
12. C11×#544C22semidirect
14. C11×#543C22semidirect
32. #10622176C22semidirect
33. #10622166C22semidirect
34. #10622163C22semidirect
37. C22×Q8×C11D4semidirect
62. C11×C22⋊Q8D4semidirect
74. C2×C11×C4⋊C4D4semidirect
112. C2×D4×C11SD16semidirect
168. #3501D11semidirect
183. C23×C11C2×SD16semidirect
223. C2×C4×C11C2×SD16semidirect
239. #544C2×D11semidirect
241. #543C2×D11semidirect
295. C22×Q8C22⋊D11semidirect
323. C22⋊Q8C22⋊D11semidirect
338. C2×C4⋊C4C22⋊D11semidirect
389. C2×D4#4325semidirect
433. C11#18196semidirect
453. C23C2×#4325semidirect
488. C2×C4C2×#4325semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
#130719722
#130675562
#130675392
#130671882
#130669342
C11×#35012
#1819611