Finite Group Databasebeta

← #14656085

Subgroups — #14656085

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2#13073529C211yesmaximal, characteristic
3#13069578C211yesmaximal, characteristic, complemented
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#461C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66991—21no—
12C2×#66983—21no—
13C2×C4×D44C2211yescharacteristic
14C11×#461—22no—
15C11×#461—22no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103—21no—
18#10622825—21no—
19#10622700—22no—
20#10622700—22no—
21#10622600—21no—
22C2×#66873—21no—
23C2×#66871—21no—
24#10622574—22no—
25#10622548C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28D4⋊(C11⋊C8)—22no—
29#10622167—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×C22⋊D11—22no—
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C2×C11×SD16—24no—
38C2×C11×SD16—42no—
39C2×C11×SD16—42no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8D412yescomplemented
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55#66991—42no—
56#66991—42no—
57#66983—42no—
58#66983—42no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11D412yes—
65C22×C11⋊C8—21no—
66C22×C11⋊C8—21no—
67C4×D44—21no—
68C4×D44—21no—
69C4×D44—21no—
70C4×D44—21no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8D412yescomplemented
73C11×#103—24no—
74C11⋊#95—22no—
75#66873—24no—
76#66871—24no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)D412yescomplemented
79C4×C11⋊C8—21no—
80C4×C11⋊C8—21no—
81#10231—111nomaximal, Sylow
82C24×C11—21no—
83C23×D11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11D812yes—
96C22×C4×C11—21no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C2×C22⋊D11—44no—
108C2×C22⋊D11—44no—
109C2×C22⋊D11—82no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44SD1612yescomplemented
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C11×SD16—48no—
125C2×C8×C11—22no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C22⋊Dic11—44no—
141(C2×D11)⋊C4—44no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—42no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—41no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—41no—
156C2×C11⋊C8—41no—
157C2×#474—111no—
158C2×#461D1111yescharacteristic, complemented
159#2537—111no—
160#1990—111no—
161C2×D4⋊C8—111no—
162C2×D4⋊C8—111no—
163#1296—111no—
164C23×C11—22no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11#12011yescharacteristic
172C22×D11—22no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179Q8×C11—42no—
180Q8×C11—42no—
181Q8×C11—81no—
182Q8×C11—81no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11—41no—
186D4×C11—41no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11—81no—
198C2×C4×C11—81no—
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12711yescharacteristic
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×SD1611yescharacteristic
207C2×C4×C11#13511yescharacteristic
208C2×C4×C11#13511yescharacteristic
209C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C11#13711yescharacteristic
213C22⋊D11—88no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220D44—22no—
221D44—22no—
222D44—41no—
223D44—41no—
224C4×D11—81no—
225C4×D11—81no—
226C4×D11—81no—
227C4×D11—81no—
228C8×C11—42no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C22×SD16—21no—
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×#121—221no—
234C2×#121—221no—
235C2×C4×D4—111no—
236C2×C4×D4C2×D1111yescharacteristic
237#474—222no—
238#474—222no—
239#461—22no—
240#461—22no—
241C2×#107—221no—
242C2×C4⋊C8—111no—
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×#103—21no—
245C2×#102—221no—
246C2×C4×C8—111no—
247#394—222no—
248#384—111no—
249#380—221no—
250#380—221no—
251#340—222no—
252D4⋊C8—222no—
253D4⋊C8—222no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11#39211yescharacteristic
262C22×C11#44711yescharacteristic
263C22×C11#44911yescharacteristic
264C22×C11#45011yescharacteristic
265C22×C11#45211yescharacteristic
266C22×C11#45511yescharacteristic
267C22×C11#45611yescharacteristic
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—82no—
278C4×C11—81no—
279C4×C11#44711yescharacteristic
280C4×C11#44811yescharacteristic
281C4×C11#44911yescharacteristic
282C4×C11#44911yescharacteristic
283C4×C11#46511yescharacteristic
284C4×C11#46611yescharacteristic
285C4×C11#46811yescharacteristic
286C4×C11#46911yescharacteristic
287Dic11—82no—
288Dic11—81no—
289C22×Q8—21no—
290C22×D4—111no—
291C22×D4—222no—
292C22×D4C22⋊D1111yescharacteristic
293C23×C4—21no—
294C23×C4—221no—
295C2×SD16—24no—
296C2×SD16—42no—
297C2×SD16—42no—
298C22×C8—21no—
299C22×C8—221no—
300C22×C8—221no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8C22⋊D1112yescomplemented
305#121—442no—
306#121—442no—
307#121—442no—
308#121—442no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4—221no—
316C4×D4—221no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4C22⋊D1111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—221no—
328C2×C42C22×D1111yescharacteristic
329#107—224no—
330C4⋊C8—21no—
331C4⋊C8—112no—
332C4⋊C8—221no—
333C4⋊C8C22⋊D1112yescomplemented
334#103—24no—
335#102—224no—
336C4×C8—221no—
337C4×C8—221no—
338#95—222no—
339C2×C11—82no—
340C2×C11#163911yescharacteristic
341C2×C11#164611yescharacteristic
342C2×C11#164711yescharacteristic
343C2×C11#165411yescharacteristic
344C2×C11#199911yescharacteristic
345C2×C11#200011yescharacteristic
346C2×C11#200711yescharacteristic
347D11—82no—
348C24—21no—
349C24—221no—
350C2×Q8—22no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—112no—
362C2×D4—221no—
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—444no—
368C2×D4—444no—
369C2×D4—882no—
370C2×D4#432312yes—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—221no—
380C22×C4—222no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4D4×D1111yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390SD16—48no—
391C2×C8—22no—
392C2×C8—41no—
393C2×C8—41no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—441no—
397C2×C8—441no—
398C2×C8—441no—
399C2×C8—441no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—442no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—444no—
416C22⋊C4—444no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C42D4×D1111yescharacteristic
420C42#434111yescharacteristic
421C42C2×C22⋊D1111yescharacteristic
422C42C2×C22⋊D1111yescharacteristic
423C11#1023111yescharacteristic, complemented, Sylow
424C23—22no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—222no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23#6699011yescharacteristic
439Q8—42no—
440Q8—42no—
441Q8—81no—
442Q8—81no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447D4—222no—
448D4—222no—
449D4—441no—
450D4—441no—
451D4—888no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—442no—
469C2×C4—441no—
470C2×C4—881no—
471C2×C4—881no—
472C2×C4—881no—
473C2×C4—881no—
474C2×C4SD16×D1111yescharacteristic
475C2×C4#6696711yescharacteristic
476C2×C4#6696811yescharacteristic
477C2×C4#6696911yescharacteristic
478C2×C4C2×#432311yescharacteristic
479C2×C4#6698511yescharacteristic
480C2×C4#6699011yescharacteristic
481C2×C4#6699111yescharacteristic
482C2×C4#6699211yescharacteristic
483C2×C4#6699211yescharacteristic
484C2×C4#6699311yescharacteristic
485C2×C4#6700211yescharacteristic
486C2×C4#6700311yescharacteristic
487C2×C4#6700611yescharacteristic
488C8—42no—
489C8—442no—
490C8—442no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22#1062264911yescharacteristic
506C22#1062265011yescharacteristic
507C22#1062278211yescharacteristic
508C22#1062278611yescharacteristic
509C22#1062281511yescharacteristic
510C22#1062281811yescharacteristic
511C22#1062283611yescharacteristic
512C4—21no—
513C4—21no—
514C4—82no—
515C4—81no—
516C4—882no—
517C4—881no—
518C4#1062265111yescharacteristic
519C4#1062265211yescharacteristic
520C4#1062278311yescharacteristic
521C4#1062278411yescharacteristic
522C4#1062278511yescharacteristic
523C4#1062278711yescharacteristic
524C4#1062283011yescharacteristic
525C4#1062285111yescharacteristic
526C2—82no—
527C2—882no—
528C2#1306779311yescharacteristic
529C2#1306784211yescharacteristic
530C2#1306784911yescharacteristic
531C2#1306789811yescharacteristic
532C2#1306961211yescharacteristic
533C2#1306961611yescharacteristic
534C2#1306966111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#461C2
socleC23×C11#120
prime radical#13073529C2
hypercenterC2×#461D11
hypocenterC11#10231
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
3. #13069578C2semidirect
4. C2×D4⋊(C11⋊C8)C2semidirect
5. C2×#10622121C2semidirect
6. #13066500C2semidirect
7. C2×C11×#461C2semidirect
44. C11×C4⋊Q8D4semidirect
72. C11×C4⋊C8D4semidirect
78. C4⋊(C11⋊C8)D4semidirect
117. C2×D44SD16semidirect
158. C2×#461D11semidirect
304. C4⋊Q8C22⋊D11semidirect
333. C4⋊C8C22⋊D11semidirect
423. C11#10231semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130735292
#130695782
C2×D4⋊(C11⋊C8)2
C2×#106221212
#130665002
C2×C11×#4612
#1023111