Finite Group Databasebeta

← #14814885

Subgroups — #14814885

Order 2816.

998 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×#10622479C212yesmaximal, complemented
2#13073558C211yesmaximal, characteristic
3#13071563C211yesmaximal, characteristic, complemented
4#13069807C212yesmaximal, complemented
5#13069801C212yesmaximal, complemented
6#13069543C211yesmaximal, characteristic, complemented
7#13069422C211yesmaximal, characteristic, complemented
8#13069410C211yesmaximal, characteristic, complemented
9#13069374C211yesmaximal, characteristic, complemented
10#13068937C212yesmaximal, complemented
11C4×C11×#106C211yesmaximal, characteristic, complemented
12C2×#66948C2212yes—
13C2×#66948C2212yes—
14C2×#66945C2212yes—
15C2×#66927—21no—
16C2×#66927C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2212yes—
24C2×#66885C2212yes—
25C2×(C2×D11)⋊C8C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27#10622600C2212yes—
28C2×#66873C2212yes—
29C2×#66873C2212yes—
30C2×#66871C2212yes—
31#10622552—21no—
32#10622552—21no—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11—21no—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622479—28no—
37#10622284—22no—
38#10622283—22no—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41#10622167C2212yes—
42C22×D44—21no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—21no—
46C22×D44D411yescharacteristic
47C22×D44C2312yes—
48C22×C4×D11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4D412yes—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×C4×Dic11—22no—
68C22×C11⋊C8C2312yes—
69#66948—24no—
70#66948—24no—
71#66948—42no—
72#66948—42no—
73#66945—24no—
74#66945—42no—
75#66927—22no—
76#66927—22no—
77#66927—44no—
78C4×D44—22no—
79C4×D44—22no—
80C11×#106—22no—
81C11×#106D414yescomplemented
82C4×C8×C11—22no—
83C11×#95—21no—
84C11×#95—21no—
85C11⋊#95—22no—
86#66885—24no—
87#66885—42no—
88(C2×D11)⋊C8—24no—
89(C2×D11)⋊C8—42no—
90#66873—24no—
91#66873—42no—
92#66871—24no—
93C4⋊(C11⋊C8)—22no—
94#26235—111nomaximal, Sylow
95C23×D11—22no—
96C23×D11C2×D412yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11C2×D412yes—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—44no—
116C2×D44—44no—
117C2×D44—44no—
118C2×D44—44no—
119C2×D44—42no—
120C2×D44—42no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—81no—
124C2×D44—81no—
125C2×D44—82no—
126C2×D44—82no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4C2×D412yes—
145C11×C4⋊C4C2×D412yes—
146C11×C4⋊C4#4112yes—
147C42×C11—42no—
148C42×C11—42no—
149C42×C11#4112yes—
150C42×C11#4112yes—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—44no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—82no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—42no—
160C4⋊Dic11—81no—
161C4×Dic11—44no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×#482—112no—
166#2541—111no—
167#2354—111no—
168#2034—112no—
169#2033—112no—
170#1982—111no—
171#1957—111no—
172#1954—111no—
173#1947—111no—
174#1875—112no—
175C4×#106D1111yescharacteristic, complemented
176C23×C11C22×D411yescharacteristic
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11#12312yes—
206C2×C4×C11#12312yes—
207C2×C4×C11#13512yes—
208C2×C4×C11AGL(1,ℤ/8)12yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221D44—42no—
222D44—42no—
223D44—42no—
224D44—42no—
225D44—44no—
226D44—84no—
227D44—88no—
228D44—88no—
229D44—84no—
230C4×D11—42no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—42no—
234C8×C11—22no—
235C8×C11—41no—
236C11⋊C8—42no—
237C2×#127—111no—
238C2×#127—221no—
239C2×#121—112no—
240C2×#121—112no—
241C2×C4×D4—111no—
242C2×#117—112no—
243#482—228no—
244C2×#107—112no—
245C2×#106C2×D1111yescharacteristic
246C2×#106C2×D1111yescharacteristic
247C2×C4⋊C8—111no—
248C2×#102—112no—
249C2×#102—112no—
250C2×#102—112no—
251C2×#102—112no—
252C2×C22⋊C8—112no—
253C2×C22⋊C8—112no—
254C2×C4×C8C2×D1111yescharacteristic
255#392—222no—
256#390—221no—
257#390—221no—
258#388—222no—
259#384—111no—
260#380—112no—
261C4×C4⋊C4—221no—
262C4×C4⋊C4C2×D1111yescharacteristic
263C4×C4⋊C4C2×D1111yescharacteristic
264#340—112no—
265#340C2×D1111yescharacteristic
266#340C2×D1111yescharacteristic
267C22×C11C2×#12311yescharacteristic
268C22×C11D4211yescharacteristic
269C22×C11#54611yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C11#57611yescharacteristic
273C22×C11#57711yescharacteristic
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—82no—
282C2×D11—82no—
283C2×D11—82no—
284C2×D11—82no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—82no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—81no—
293C4×C11#48214yescomplemented
294C4×C11#53211yescharacteristic
295C4×C11#54011yescharacteristic
296C4×C11#55011yescharacteristic
297C4×C11#55911yescharacteristic
298Dic11—42no—
299Dic11—82no—
300C22×D4—111no—
301C22×D4—112no—
302C22×D4—222no—
303C22×D4—222no—
304C22×D4—221no—
305C22×D4—221no—
306C23×C4—112no—
307C22×C8—112no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310#127—222no—
311#127—222no—
312#127—444no—
313#121—224no—
314#121—224no—
315#121—442no—
316#121—442no—
317C4×D4—222no—
318C4×D4—222no—
319#117—224no—
320#117—442no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—112no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—222no—
337C2×C42C22×D1111yescharacteristic
338#107—224no—
339#106—22no—
340#106D4414yescomplemented
341C4⋊C8—222no—
342#102—224no—
343#102—224no—
344#102—442no—
345#102—442no—
346C22⋊C8—224no—
347C22⋊C8—442no—
348C4×C8—22no—
349#95—21no—
350#95—21no—
351#95—222no—
352C2×C11#244511yescharacteristic
353C2×C11C2×#48211yescharacteristic
354C2×C11#309611yescharacteristic
355C2×C11#327411yescharacteristic
356C2×C11#328411yescharacteristic
357C2×C11#330511yescharacteristic
358C2×C11#332411yescharacteristic
359D11—82no—
360D11—162no—
361C24—112no—
362C24—222no—
363C2×D4—222no—
364C2×D4—222no—
365C2×D4—222no—
366C2×D4—222no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—444no—
373C2×D4—444no—
374C2×D4—444no—
375C2×D4—444no—
376C2×D4—442no—
377C2×D4—442no—
378C2×D4—442no—
379C2×D4—442no—
380C2×D4—881no—
381C2×D4—881no—
382C2×D4—882no—
383C2×D4—882no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—112no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4D4×D1111yescharacteristic
397C22×C4D4×D1111yescharacteristic
398C22×C4C23×D1111yescharacteristic
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8C2×D4412yes—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—442no—
417C4⋊C4—881no—
418C4⋊C4C2×D4412yes—
419C4⋊C4C2×D4412yes—
420C4⋊C4#433912yes—
421C22⋊C4—224no—
422C22⋊C4—444no—
423C22⋊C4—444no—
424C22⋊C4—444no—
425C22⋊C4—882no—
426C42—42no—
427C42—42no—
428C42—444no—
429C42#433912yes—
430C42#434312yes—
431C11#2623511yescharacteristic, complemented, Sylow
432C23—222no—
433C23—222no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23—442no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23C2×D4×D1111yescharacteristic
447D4—444no—
448D4—442no—
449D4—442no—
450D4—442no—
451D4—442no—
452D4—884no—
453D4—888no—
454D4—888no—
455D4—884no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4#6694712yes—
481C2×C4#6694712yes—
482C2×C4#6696712yes—
483C2×C4#6696912yes—
484C2×C4C22×D4411yescharacteristic
485C2×C4C2×#433911yescharacteristic
486C2×C4C2×#433911yescharacteristic
487C2×C4C2×#434311yescharacteristic
488C2×C4#6704211yescharacteristic
489C2×C4#6704211yescharacteristic
490C8—22no—
491C8—41no—
492C8—442no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22—442no—
498C22—442no—
499C22—442no—
500C22—882no—
501C22—882no—
502C22—882no—
503C22—882no—
504C22—882no—
505C22—882no—
506C22—882no—
507C22C2×#6694711yescharacteristic
508C22D4×D4411yescharacteristic
509C22#1062308111yescharacteristic
510C22C2×#6696711yescharacteristic
511C22C2×#6696911yescharacteristic
512C22#1062330011yescharacteristic
513C22#1062330111yescharacteristic
514C4—22no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—81no—
519C4—442no—
520C4—882no—
521C4#1062247914yescomplemented
522C4#1062300811yescharacteristic
523C4#1062306611yescharacteristic
524C4#1062310811yescharacteristic
525C4#1062311611yescharacteristic
526C2—882no—
527C2—1762no—
528C2#1307238111yescharacteristic
529C2C2×#1062247911yescharacteristic
530C2#1307857711yescharacteristic
531C2#1308023711yescharacteristic
532C2#1308034711yescharacteristic
533C2#1308056811yescharacteristic
534C2#1308084911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#106C2
socleC23×C11C22×D4
prime radical#13073558C2
hypercenterC4×#106D11
hypocenterC11#26235
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
1. C2×#10622479C2semidirect
3. #13071563C2semidirect
4. #13069807C2semidirect
5. #13069801C2semidirect
6. #13069543C2semidirect
7. #13069422C2semidirect
8. #13069410C2semidirect
9. #13069374C2semidirect
10. #13068937C2semidirect
11. C4×C11×#106C2semidirect
81. C11×#106D4semidirect
175. C4×#106D11semidirect
293. C4×C11#482semidirect
340. #106D44semidirect
431. C11#26235semidirect
521. C4#10622479semidirect

Maximal subgroups

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

subgroupindex
C2×#106224792
#130735582
#130715632
#130698072
#130698012
#130695432
#130694222
#130694102
#130693742
#130689372
C4×C11×#1062
#2623511