Finite Group Databasebeta

← #14649435

Subgroups — #14649435

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊C8C211yesmaximal, 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—
12C22×C8×D11—21no—
13C2×C42×D11C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16#10622834—21no—
17#10622834—21no—
18#10622834C412yes—
19C2×(C2×D11)⋊C8—21no—
20C2×Dic11⋊C8—21no—
21#10622548C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24D11×C4⋊C8—22no—
25D11×C4⋊C8—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—44no—
47#66991—42no—
48#66991—42no—
49#66991—42no—
50#66991—42no—
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—
59C2×C8×D11—24no—
60C2×C8×D11—42no—
61C2×C8×D11—42no—
62C42×D11—21no—
63C42×D11—21no—
64C42×D11—21no—
65C42×D11—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yescomplemented
70(C2×D11)⋊C8—42no—
71Dic11⋊C8—24no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yescomplemented
76#9133—111nomaximal, Sylow
77C24×C11—22no—
78C23×D11C22⋊C411yescharacteristic
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
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—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—44no—
99C2×C22⋊D11—44no—
100C2×C22⋊D11—44no—
101C22×Dic11—22no—
102C22×Dic11C22⋊C411yescharacteristic
103C22×Dic11C22⋊C411yescharacteristic
104C22×Dic11C22⋊C411yescharacteristic
105C2×C4×D11—22no—
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—41no—
117C2×C4×D11D812yes—
118C2×C4×D11D812yes—
119C2×C4×D11SD1612yes—
120C2×C4×D11SD1612yes—
121C2×C8×C11—22no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130C42×C11#4111yescharacteristic
131C22⋊Dic11—44no—
132C22⋊Dic11—44no—
133C22⋊Dic11—44no—
134C4⋊Dic11—42no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138C4⋊Dic11—41no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144C4×Dic11—21no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—41no—
150C2×C11⋊C8—41no—
151C8×D11—48no—
152C22×C4⋊C8—111no—
153#2856—111no—
154#1797—111no—
155C2×#331—111no—
156C2×#331D1111yescharacteristic, complemented
157#1296—111no—
158#1296—111no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11C2×C22⋊C411yescharacteristic
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—21no—
171C22×D11#10012yes—
172C22×D11#10212yes—
173C22×D11#10212yes—
174D4×C11—82no—
175D4×C11—82no—
176D4×C11—81no—
177D4×C11—81no—
178D4×C11—81no—
179D4×C11—81no—
180D4×C11—81no—
181D4×C11—81no—
182D4×C11—81no—
183D4×C11—81no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11C4×D411yescharacteristic
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12311yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C2×SD1611yescharacteristic
195C2×C4×C11C2×SD1611yescharacteristic
196C2×C4×C11#13511yescharacteristic
197C2×C4×C11#13511yescharacteristic
198C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C11#13711yescharacteristic
200C22⋊D11—88no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11#10212yes—
212C2×Dic11#10212yes—
213C4×D11—22no—
214C4×D11—22no—
215C4×D11—22no—
216C4×D11—22no—
217C4×D11—22no—
218C4×D11—22no—
219C4×D11—22no—
220C4×D11—22no—
221C4×D11—42no—
222C4×D11—42no—
223C8×C11—42no—
224C8×C11—81no—
225C11⋊C8—42no—
226C11⋊C8—81no—
227C23×C8—221no—
228C2×#127C2×D1111yescharacteristic
229C2×#121—112no—
230C2×#121—221no—
231C2×#121—221no—
232C22×C42—111no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8—111no—
235C2×C4⋊C8—222no—
236C2×C4⋊C8—221no—
237C2×C4⋊C8—222no—
238C2×C4⋊C8C2×D1111yescharacteristic
239C2×C4⋊C8C2×D1111yescharacteristic
240C2×C22⋊C8—221no—
241#390—112no—
242#390—221no—
243#390—221no—
244#384—111no—
245#336—221no—
246#331—22no—
247#331—222no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11#38611yescharacteristic
256C22×C11C2×#10011yescharacteristic
257C22×C11#41311yescharacteristic
258C22×C11C2×#10211yescharacteristic
259C22×C11C2×#10211yescharacteristic
260C22×C11#41611yescharacteristic
261C22×C11#41711yescharacteristic
262C2×D11—22no—
263C2×D11—22no—
264C2×D11—22no—
265C2×D11—22no—
266C2×D11—22no—
267C2×D11—22no—
268C2×D11#33114yescomplemented
269C4×C11—21no—
270C4×C11—21no—
271C4×C11#44711yescharacteristic
272C4×C11#44811yescharacteristic
273C4×C11#46511yescharacteristic
274C4×C11#46511yescharacteristic
275C4×C11#46611yescharacteristic
276C4×C11#46611yescharacteristic
277C4×C11#48011yescharacteristic
278C4×C11#48111yescharacteristic
279Dic11—22no—
280Dic11—22no—
281Dic11—41no—
282Dic11—82no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—222no—
286C22×D4C4×D1112yes—
287C23×C4—111no—
288C23×C4—111no—
289C23×C4—111no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—224no—
293C22×C8—221no—
294C22×C8—221no—
295C22×C8—442no—
296C22×C8—442no—
297#127—21no—
298#127—21no—
299#127—21no—
300#127—21no—
301#121—442no—
302#121—442no—
303#121—442no—
304#121—442no—
305#121—444no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C22⋊C4—222no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—222no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—221no—
316C2×C42—221no—
317C2×C42—221no—
318C2×C42—221no—
319C2×C42C22×D1111yescharacteristic
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8—112no—
324C4⋊C8—224no—
325C4⋊C8—221no—
326C4⋊C8—221no—
327C4⋊C8—221no—
328C4⋊C8C22⋊D1112yescomplemented
329C22⋊C8—442no—
330C2×C11—162no—
331C2×C11C2×#33111yescharacteristic
332C2×C11#154011yescharacteristic
333C2×C11#154711yescharacteristic
334C2×C11#155111yescharacteristic
335C2×C11#187411yescharacteristic
336C2×C11#189311yescharacteristic
337C2×C11#190011yescharacteristic
338D11—24no—
339C24—22no—
340C24—111no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—444no—
358C2×D4—444no—
359C2×D4—444no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—112no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—112no—
366C22×C4—111no—
367C22×C4—222no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—222no—
379C22×C4—441no—
380C22×C4C2×C4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383C2×C8—22no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—222no—
390C2×C8—448no—
391C2×C8—441no—
392C2×C8—441no—
393C2×C8—441no—
394C2×C8—441no—
395C2×C8—441no—
396C4⋊C4—442no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C22⋊C4—444no—
402C22⋊C4—444no—
403C22⋊C4—444no—
404C42—221no—
405C42—221no—
406C42—221no—
407C42—221no—
408C42—221no—
409C42—221no—
410C42#433911yescharacteristic
411C42D4×D1111yescharacteristic
412C42#434111yescharacteristic
413C42C2×C22⋊D1111yescharacteristic
414C11#913311yescharacteristic, complemented, Sylow
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—112no—
423C23—112no—
424C23—112no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23C22⋊C4×D1111yescharacteristic
430D4—82no—
431D4—82no—
432D4—81no—
433D4—81no—
434D4—81no—
435D4—81no—
436D4—81no—
437D4—81no—
438D4—81no—
439D4—81no—
440D4—888no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—112no—
444C2×C4—112no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4(C22⋊D11)⋊C411yescharacteristic
466C2×C4#6693611yescharacteristic
467C2×C4#6693711yescharacteristic
468C2×C4D8×D1111yescharacteristic
469C2×C4D8×D1111yescharacteristic
470C2×C4#6696411yescharacteristic
471C2×C4#6696511yescharacteristic
472C2×C4SD16×D1111yescharacteristic
473C2×C4SD16×D1111yescharacteristic
474C2×C4#6696811yescharacteristic
475C2×C4#6696911yescharacteristic
476C2×C4C4×C22⋊D1111yescharacteristic
477C2×C4#6699011yescharacteristic
478C2×C4#6699111yescharacteristic
479C8—42no—
480C8—81no—
481C8—442no—
482C8—881no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—114no—
491C22—222no—
492C22—222no—
493C22—222no—
494C22—222no—
495C22—222no—
496C22—222no—
497C22D11×#10011yescharacteristic
498C22#1062235811yescharacteristic
499C22D11×#10211yescharacteristic
500C22D11×#10211yescharacteristic
501C22#1062238411yescharacteristic
502C22#1062238511yescharacteristic
503C22#1062256911yescharacteristic
504C4—21no—
505C4—21no—
506C4—222no—
507C4—222no—
508C4—441no—
509C4—882no—
510C4#1062238711yescharacteristic
511C4#1062238811yescharacteristic
512C4#1062239011yescharacteristic
513C4#1062239111yescharacteristic
514C4#1062276911yescharacteristic
515C4#1062277011yescharacteristic
516C4#1062278311yescharacteristic
517C4#1062278411yescharacteristic
518C2—162no—
519C2—224no—
520C2D11×#33111yescharacteristic
521C2#1306726211yescharacteristic
522C2#1306729011yescharacteristic
523C2#1306730811yescharacteristic
524C2#1306893011yescharacteristic
525C2#1306904111yescharacteristic
526C2#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#9133
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×D11×C4⋊C8C2semidirect
3. #13068593C2semidirect
4. C2×#10622182C2semidirect
5. #13066500C2semidirect
6. #13066500C2semidirect
7. C2×C11×#331C2semidirect
69. C11×C4⋊C8D4semidirect
75. C4⋊(C11⋊C8)D4semidirect
156. C2×#331D11semidirect
268. C2×D11#331semidirect
328. C4⋊C8C22⋊D11semidirect
414. C11#9133semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊C82
#130769582
#130685932
C2×#106221822
#130665002
C2×C11×#3312
#913311