Finite Group Databasebeta

← #14649480

Subgroups — #14649480

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#13076958C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic, complemented
4C2×#10622182C211yesmaximal, characteristic, complemented
5#13066500C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×#66991—21no—
10C2×#66991—21no—
11C2×#66991C412yes—
12C2×C42×D11C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15#10622834—21no—
16#10622834—21no—
17#10622834C412yes—
18C2×(C2×D11)⋊C8—21no—
19C2×(C2×D11)⋊C8—21no—
20C2×#66879—21no—
21#10622548C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622448—22no—
25#10622448—22no—
26C11×#331—22no—
27#10622188—21no—
28#10622182—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11C2×C412yes—
32C22×C22⋊D11—22no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C2×C42×C11C2311yescharacteristic
43C2×C22⋊Dic11—22no—
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11—22no—
46#66991—42no—
47#66991—42no—
48#66991—42no—
49#66991—42no—
50#66991—44no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11C2×C412yes—
54C2×C4×Dic11C2×C411yescharacteristic
55C2×C4×Dic11D411yescharacteristic
56C2×C4×Dic11D411yescharacteristic
57C22×C11⋊C8—21no—
58C22×C11⋊C8—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
75C24×C11—22no—
76C23×D11C22⋊C411yescharacteristic
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C2×C22⋊D11—44no—
97C2×C22⋊D11—44no—
98C2×C22⋊D11—44no—
99C22×Dic11—22no—
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C22×Dic11C22⋊C411yescharacteristic
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—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128C42×C11#4111yescharacteristic
129C22⋊Dic11—44no—
130C22⋊Dic11—44no—
131C22⋊Dic11—44no—
132C4⋊Dic11—42no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
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×#331D1111yescharacteristic, complemented
154#1296—111no—
155#1296—111no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11C2×C22⋊C411yescharacteristic
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—21no—
170C22×D11#10012yes—
171D4×C11—82no—
172D4×C11—82no—
173D4×C11—81no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177D4×C11—81no—
178D4×C11—81no—
179D4×C11—81no—
180D4×C11—81no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11C4×D411yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12311yescharacteristic
189C2×C4×C11#13511yescharacteristic
190C2×C4×C11#13511yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C11#13711yescharacteristic
197C22⋊D11—88no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
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×#127C2×D1111yescharacteristic
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#384—111no—
242#336—221no—
243#331—22no—
244#331—222no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11#38611yescharacteristic
253C22×C11C2×#10011yescharacteristic
254C22×C11#41311yescharacteristic
255C22×C11#41611yescharacteristic
256C22×C11#41711yescharacteristic
257C22×C11#41811yescharacteristic
258C22×C11#41811yescharacteristic
259C2×D11—22no—
260C2×D11—22no—
261C2×D11—22no—
262C2×D11—41no—
263C2×D11—41no—
264C2×D11—41no—
265C2×D11—41no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11#44911yescharacteristic
269C4×C11#44911yescharacteristic
270C4×C11#46811yescharacteristic
271C4×C11#46811yescharacteristic
272C4×C11#46911yescharacteristic
273C4×C11#46911yescharacteristic
274C4×C11#48211yescharacteristic
275C4×C11#48211yescharacteristic
276Dic11—41no—
277Dic11—41no—
278Dic11—41no—
279Dic11—82no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—222no—
283C22×D4C4×D1112yes—
284C23×C4—111no—
285C23×C4—111no—
286C23×C4—111no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—221no—
290C22×C8—221no—
291#127—21no—
292#127—21no—
293#127—21no—
294#127—21no—
295#121—444no—
296#121—442no—
297#121—442no—
298#121—442no—
299#121—442no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
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⋊C8C22⋊D1112yescomplemented
322C22⋊C8—224no—
323C22⋊C8—442no—
324#97—224no—
325C2×C11—162no—
326C2×C11#155111yescharacteristic
327C2×C11#155311yescharacteristic
328C2×C11#155511yescharacteristic
329C2×C11#155711yescharacteristic
330C2×C11#187511yescharacteristic
331C2×C11#189511yescharacteristic
332C2×C11#190011yescharacteristic
333D11—42no—
334C24—22no—
335C24—111no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—444no—
353C2×D4—444no—
354C2×D4—444no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—222no—
359C22×C4—221no—
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—222no—
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—442no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C22⋊C4—444no—
396C22⋊C4—444no—
397C22⋊C4—444no—
398C42—221no—
399C42—221no—
400C42—221no—
401C42—221no—
402C42—221no—
403C42—221no—
404C42#433911yescharacteristic
405C42D4×D1111yescharacteristic
406C42#434111yescharacteristic
407C42C2×C22⋊D1111yescharacteristic
408C11#914211yescharacteristic, complemented, Sylow
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—112no—
417C23—221no—
418C23—221no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23C22⋊C4×D1111yescharacteristic
424D4—82no—
425D4—82no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
432D4—81no—
433D4—81no—
434D4—888no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4(C22⋊D11)⋊C411yescharacteristic
460C2×C4#6693611yescharacteristic
461C2×C4#6693711yescharacteristic
462C2×C4#6696411yescharacteristic
463C2×C4#6696411yescharacteristic
464C2×C4#6696411yescharacteristic
465C2×C4#6696511yescharacteristic
466C2×C4#6696711yescharacteristic
467C2×C4#6696711yescharacteristic
468C2×C4#6696811yescharacteristic
469C2×C4#6696911yescharacteristic
470C2×C4C4×C22⋊D1111yescharacteristic
471C2×C4#6699011yescharacteristic
472C2×C4#6699111yescharacteristic
473C8—42no—
474C8—81no—
475C8—442no—
476C8—881no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—222no—
485C22—222no—
486C22—222no—
487C22—441no—
488C22—441no—
489C22—441no—
490C22—441no—
491C22D11×#10011yescharacteristic
492C22#1062235811yescharacteristic
493C22#1062238311yescharacteristic
494C22#1062238311yescharacteristic
495C22#1062238411yescharacteristic
496C22#1062238511yescharacteristic
497C22#1062256911yescharacteristic
498C4—21no—
499C4—21no—
500C4—441no—
501C4—441no—
502C4—441no—
503C4—882no—
504C4#1062239211yescharacteristic
505C4#1062239311yescharacteristic
506C4#1062239511yescharacteristic
507C4#1062239711yescharacteristic
508C4#1062277111yescharacteristic
509C4#1062277211yescharacteristic
510C4#1062278511yescharacteristic
511C4#1062278711yescharacteristic
512C2—162no—
513C2—442no—
514C2#1306730811yescharacteristic
515C2#1306731811yescharacteristic
516C2#1306732811yescharacteristic
517C2#1306733511yescharacteristic
518C2#1306893511yescharacteristic
519C2#1306905111yescharacteristic
520C2#1306907611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11C2×C22⋊C4
prime radical#13076958C2
cosocleC2×C42×C11C23
hypercenterC2×#331D11
hypocenterC11#9142
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. C2×#10622448C2semidirect
3. #13068593C2semidirect
4. C2×#10622182C2semidirect
5. #13066500C2semidirect
6. #13066500C2semidirect
7. C2×C11×#331C2semidirect
66. C11×C4⋊C8D4semidirect
73. C4⋊(C11⋊C8)D4semidirect
153. C2×#331D11semidirect
321. C4⋊C8C22⋊D11semidirect
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
#130769582
#130685932
C2×#106221822
#130665002
C2×C11×#3312
#914211