Finite Group Databasebeta

← #14649482

Subgroups — #14649482

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622448C211yesmaximal, characteristic, complemented
2#13076962C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic, complemented
4C2×#10622123C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×#66948—21no—
9C2×#66948—21no—
10C2×#66948C412yes—
11C2×#66927C2211yescharacteristic
12C2×C42×D11C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C11×#384C2211yescharacteristic
16C2×(C2×D11)⋊C8—21no—
17C2×(C2×D11)⋊C8—21no—
18C2×#66879—21no—
19#10622601—21no—
20#10622601—21no—
21#10622601C412yes—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622448—22no—
25#10622448—22no—
26#10622188—21no—
27#10622123—22no—
28#10622123—22no—
29C22×D44—22no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44C2×C412yes—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66948—44no—
51#66948—42no—
52#66948—42no—
53#66948—42no—
54#66948—42no—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58#66927—21no—
59C42×D11—21no—
60C42×D11—21no—
61C42×D11—21no—
62C42×D11—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yescomplemented
67(C2×D11)⋊C8—24no—
68(C2×D11)⋊C8—42no—
69#66879—24no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yescomplemented
74#9142—111nomaximal, Sylow
75C23×D11—22no—
76C23×D11C22⋊C411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—44no—
89C2×D44—44no—
90C2×D44—44no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×C4×D11—22no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11—41no—
119C2×C8×C11—22no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11#4111yescharacteristic
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—44no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C2×#432—111no—
150#2856—111no—
151#1797—111no—
152C2×#331—111no—
153C2×#331—111no—
154#1296—111no—
155#1296D1111yescharacteristic, complemented
156C23×C11C2×C22⋊C411yescharacteristic
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—42no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—42no—
170C22×D11#10012yes—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C4×D411yescharacteristic
177C2×C4×C11C4×D411yescharacteristic
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12311yescharacteristic
182C2×C4×C11#13511yescharacteristic
183C2×C4×C11#13511yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11#13711yescharacteristic
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199D44—82no—
200D44—82no—
201D44—88no—
202D44—81no—
203D44—81no—
204D44—81no—
205D44—81no—
206D44—81no—
207D44—81no—
208D44—81no—
209D44—81no—
210C4×D11—42no—
211C4×D11—42no—
212C4×D11—41no—
213C4×D11—41no—
214C4×D11—41no—
215C4×D11—41no—
216C4×D11—41no—
217C4×D11—41no—
218C4×D11—41no—
219C4×D11—41no—
220C8×C11—42no—
221C8×C11—81no—
222C11⋊C8—42no—
223C11⋊C8—81no—
224C2×#127—111no—
225C2×#121—112no—
226C2×#121—221no—
227C2×#121—221no—
228C22×C42—111no—
229#432—222no—
230#432—222no—
231C2×C4⋊C8—111no—
232C2×C4⋊C8—111no—
233C2×C4⋊C8C2×D1111yescharacteristic
234C2×C4⋊C8C2×D1111yescharacteristic
235C2×C22⋊C8—221no—
236C2×C22⋊C8—221no—
237C2×#97—221no—
238#390—112no—
239#390—221no—
240#390—221no—
241#384C2×D1111yescharacteristic
242#336—221no—
243#331—222no—
244#331—222no—
245C22×C11#38611yescharacteristic
246C22×C11C2×#10011yescharacteristic
247C22×C11#41311yescharacteristic
248C22×C11#41611yescharacteristic
249C22×C11#41711yescharacteristic
250C22×C11#41811yescharacteristic
251C22×C11#41811yescharacteristic
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—82no—
260C2×D11—82no—
261C2×D11—82no—
262C2×D11—82no—
263C2×D11—82no—
264C2×D11—82no—
265C2×D11—82no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—82no—
269C4×C11#44911yescharacteristic
270C4×C11#44911yescharacteristic
271C4×C11#46811yescharacteristic
272C4×C11#46811yescharacteristic
273C4×C11#46911yescharacteristic
274C4×C11#46911yescharacteristic
275C4×C11#48211yescharacteristic
276C4×C11#48211yescharacteristic
277Dic11—41no—
278Dic11—41no—
279Dic11—41no—
280C22×D4—112no—
281C22×D4—222no—
282C22×D4—221no—
283C22×D4—221no—
284C23×C4—111no—
285C23×C4—111no—
286C23×C4—111no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—221no—
290C22×C8—221no—
291#127—221no—
292#127—221no—
293#127—221no—
294#127—221no—
295#121—444no—
296#121—442no—
297#121—442no—
298#121—442no—
299#121—442no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4C4×D1112yes—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C42—111no—
307C2×C42—111no—
308C2×C42—111no—
309C2×C42—221no—
310C2×C42—221no—
311C2×C42—221no—
312C2×C42—221no—
313C2×C42C22×D1111yescharacteristic
314C4⋊C8—21no—
315C4⋊C8—21no—
316C4⋊C8—21no—
317C4⋊C8—112no—
318C4⋊C8—221no—
319C4⋊C8—221no—
320C4⋊C8—221no—
321C4⋊C8D4412yescomplemented
322C22⋊C8—224no—
323C22⋊C8—442no—
324#97—224no—
325C2×C11#155111yescharacteristic
326C2×C11#155311yescharacteristic
327C2×C11#155511yescharacteristic
328C2×C11#155711yescharacteristic
329C2×C11#187511yescharacteristic
330C2×C11#189511yescharacteristic
331C2×C11#190011yescharacteristic
332D11—42no—
333D11—162no—
334C24—111no—
335C24—222no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—442no—
339C2×D4—442no—
340C2×D4—444no—
341C2×D4—444no—
342C2×D4—444no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—441no—
355C22×C4—22no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—222no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—441no—
375C22×C4C2×C4×D1111yescharacteristic
376C22×C4D4×D1111yescharacteristic
377C22×C4D4×D1111yescharacteristic
378C2×C8—22no—
379C2×C8—41no—
380C2×C8—41no—
381C2×C8—41no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—222no—
385C2×C8—441no—
386C2×C8—441no—
387C2×C8—441no—
388C2×C8—441no—
389C2×C8—441no—
390C4⋊C4—42no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C22⋊C4—444no—
396C22⋊C4—444no—
397C22⋊C4—444no—
398C42—221no—
399C42—221no—
400C42—221no—
401C42—221no—
402C42—221no—
403C42—221no—
404C42C2×D4411yescharacteristic
405C42#433911yescharacteristic
406C42D4×D1111yescharacteristic
407C42#434311yescharacteristic
408C11#914211yescharacteristic, complemented, Sylow
409C23—112no—
410C23—221no—
411C23—221no—
412C23—221no—
413C23—221no—
414C23—221no—
415C23—221no—
416C23—442no—
417C23—442no—
418C23—442no—
419C23—442no—
420C23—442no—
421C23—442no—
422C23—442no—
423C23C22⋊C4×D1111yescharacteristic
424D4—882no—
425D4—882no—
426D4—888no—
427D4—881no—
428D4—881no—
429D4—881no—
430D4—881no—
431D4—881no—
432D4—881no—
433D4—881no—
434D4—881no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4C4×D4411yescharacteristic
460C2×C4#6693511yescharacteristic
461C2×C4#6693711yescharacteristic
462C2×C4#6694611yescharacteristic
463C2×C4#6694711yescharacteristic
464C2×C4#6694811yescharacteristic
465C2×C4#6696411yescharacteristic
466C2×C4#6696411yescharacteristic
467C2×C4#6696711yescharacteristic
468C2×C4#6696711yescharacteristic
469C2×C4#6696711yescharacteristic
470C2×C4#6696911yescharacteristic
471C2×C4#6697111yescharacteristic
472C2×C4#6697211yescharacteristic
473C8—42no—
474C8—81no—
475C8—442no—
476C8—881no—
477C22—222no—
478C22—222no—
479C22—222no—
480C22—441no—
481C22—441no—
482C22—441no—
483C22—441no—
484C22—882no—
485C22—882no—
486C22—882no—
487C22—882no—
488C22—882no—
489C22—882no—
490C22—882no—
491C22#1062227811yescharacteristic
492C22D11×#10011yescharacteristic
493C22#1062236411yescharacteristic
494C22#1062238311yescharacteristic
495C22#1062238311yescharacteristic
496C22#1062241611yescharacteristic
497C22#1062241711yescharacteristic
498C4—21no—
499C4—21no—
500C4—82no—
501C4—441no—
502C4—441no—
503C4—441no—
504C4#1062239411yescharacteristic
505C4#1062239511yescharacteristic
506C4#1062242411yescharacteristic
507C4#1062242511yescharacteristic
508C4#1062247811yescharacteristic
509C4#1062247911yescharacteristic
510C4#1062249811yescharacteristic
511C4#1062249911yescharacteristic
512C2—442no—
513C2—1762no—
514C2#1306731011yescharacteristic
515C2#1306732011yescharacteristic
516C2#1306732811yescharacteristic
517C2#1306733711yescharacteristic
518C2#1306893711yescharacteristic
519C2#1306905311yescharacteristic
520C2#1306907811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11C2×C22⋊C4
prime radical#13076962C2
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#9142
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. C2×#10622448C2semidirect
3. #13068593C2semidirect
4. C2×#10622123C2semidirect
5. C2×#10622123C2semidirect
6. #13066499C2semidirect
7. C11×#1296C2semidirect
66. C11×C4⋊C8D4semidirect
73. C4⋊(C11⋊C8)D4semidirect
155. #1296D11semidirect
321. C4⋊C8D44semidirect
408. C11#9142semidirect

Maximal subgroups

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

subgroupindex
C2×#106224482
#130769622
#130685932
C2×#106221232
#130664992
C11×#12962
#914211