Finite Group Databasebeta

← #14649477

Subgroups — #14649477

Order 2816.

752 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×#10622450C211yesmaximal, 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
8C22×#4313—21no—
9C2×#66948—21no—
10C2×#66948—21no—
11C2×#66948C412yes—
12C2×#66927C2211yescharacteristic
13C2×C42×D11C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C11×#384C2211yescharacteristic
17C2×(C2×D11)⋊C8—21no—
18C2×Dic11⋊C8—21no—
19#10622601—21no—
20#10622601—21no—
21#10622601C412yes—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622450—22no—
25#10622450—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—
50C2×#4313—24no—
51C2×#4313—42no—
52C2×#4313—42no—
53#66948—42no—
54#66948—42no—
55#66948—42no—
56#66948—42no—
57#66948—44no—
58#66927—21no—
59#66927—21no—
60#66927—21no—
61#66927—21no—
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#9141—111nomaximal, Sylow
77C23×D11—22no—
78C23×D11C22⋊C411yescharacteristic
79C22×C4×C11—22no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—44no—
91C2×D44—44no—
92C2×D44—44no—
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×D44—41no—
104C2×D44—41no—
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—21no—
117C2×C4×D11—21no—
118C2×C4×D11—41no—
119C2×C4×D11D812yes—
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—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11#4111yescharacteristic
135C42×C11#4111yescharacteristic
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—44no—
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—
151#4313—48no—
152C2×#423—111no—
153#2856—111no—
154#1797—111no—
155C2×#331—111no—
156C2×#331—111no—
157#1296—111no—
158#1296D1111yescharacteristic, complemented
159C23×C11C2×C22⋊C411yescharacteristic
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—42no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—42no—
173C22×D11#10212yes—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11C4×D411yescharacteristic
180C2×C4×C11C4×D411yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12311yescharacteristic
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C2×SD1611yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11#13711yescharacteristic
192C2×C4×C11#13711yescharacteristic
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11#10012yes—
201C2×Dic11#10212yes—
202D44—82no—
203D44—82no—
204D44—88no—
205D44—81no—
206D44—81no—
207D44—81no—
208D44—81no—
209D44—81no—
210D44—81no—
211D44—81no—
212D44—81no—
213C4×D11—22no—
214C4×D11—22no—
215C4×D11—22no—
216C4×D11—22no—
217C4×D11—42no—
218C4×D11—42no—
219C4×D11—41no—
220C4×D11—41no—
221C4×D11—41no—
222C4×D11—41no—
223C8×C11—42no—
224C8×C11—81no—
225C11⋊C8—42no—
226C11⋊C8—81no—
227C22×M16—221no—
228C2×#127—111no—
229C2×#121—112no—
230C2×#121—221no—
231C2×#121—221no—
232C22×C42—111no—
233#423—222no—
234#423—222no—
235C2×C4⋊C8—111no—
236C2×C4⋊C8—111no—
237C2×C4⋊C8—221no—
238C2×C4⋊C8C2×D1111yescharacteristic
239C2×C4⋊C8C2×D1111yescharacteristic
240C2×C22⋊C8—221no—
241#390—112no—
242#390—221no—
243#390—221no—
244#384C2×D1111yescharacteristic
245#336—221no—
246#331—222no—
247#331—222no—
248C22×C11#38611yescharacteristic
249C22×C11C2×#10011yescharacteristic
250C22×C11#41311yescharacteristic
251C22×C11C2×#10211yescharacteristic
252C22×C11#41711yescharacteristic
253C22×C11#41711yescharacteristic
254C22×C11#41811yescharacteristic
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—82no—
263C2×D11—82no—
264C2×D11—82no—
265C2×D11—82no—
266C2×D11—82no—
267C2×D11—82no—
268C2×D11—82no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—82no—
272C4×C11#44711yescharacteristic
273C4×C11#44811yescharacteristic
274C4×C11#46811yescharacteristic
275C4×C11#46811yescharacteristic
276C4×C11#46911yescharacteristic
277C4×C11#46911yescharacteristic
278C4×C11#48011yescharacteristic
279C4×C11#48111yescharacteristic
280Dic11—22no—
281Dic11—22no—
282Dic11—41no—
283C22×D4—112no—
284C22×D4—222no—
285C22×D4—221no—
286C22×D4—221no—
287C23×C4—111no—
288C23×C4—111no—
289C23×C4—111no—
290C2×M16—224no—
291C2×M16—442no—
292C2×M16—442no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—221no—
296C22×C8—221no—
297#127—221no—
298#127—221no—
299#127—221no—
300#127—221no—
301#121—442no—
302#121—442no—
303#121—442no—
304#121—442no—
305#121—444no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4C4×D1112yes—
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⋊C8D4412yescomplemented
329C22⋊C8—442no—
330C2×C11#154511yescharacteristic
331C2×C11#154711yescharacteristic
332C2×C11#155711yescharacteristic
333C2×C11#156011yescharacteristic
334C2×C11#187411yescharacteristic
335C2×C11#189511yescharacteristic
336C2×C11#190011yescharacteristic
337D11—42no—
338D11—162no—
339C24—111no—
340C24—222no—
341C2×D4—222no—
342C2×D4—222no—
343C2×D4—442no—
344C2×D4—442no—
345C2×D4—444no—
346C2×D4—444no—
347C2×D4—444no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—441no—
360C22×C4—22no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—111no—
366C22×C4—222no—
367C22×C4—221no—
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—221no—
379C22×C4—441no—
380C22×C4C2×C4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383M16—448no—
384C2×C8—22no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—41no—
390C2×C8—222no—
391C2×C8—441no—
392C2×C8—441no—
393C2×C8—441no—
394C2×C8—441no—
395C2×C8—441no—
396C4⋊C4—42no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C22⋊C4—444no—
402C22⋊C4—444no—
403C22⋊C4—444no—
404C42—221no—
405C42—221no—
406C42—221no—
407C42—221no—
408C42—221no—
409C42—221no—
410C42C2×D4411yescharacteristic
411C42#433911yescharacteristic
412C42D4×D1111yescharacteristic
413C42#434311yescharacteristic
414C11#914111yescharacteristic, complemented, Sylow
415C23—112no—
416C23—221no—
417C23—221no—
418C23—221no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23—442no—
423C23—442no—
424C23—442no—
425C23—442no—
426C23—442no—
427C23—442no—
428C23—442no—
429C23C22⋊C4×D1111yescharacteristic
430D4—882no—
431D4—882no—
432D4—888no—
433D4—881no—
434D4—881no—
435D4—881no—
436D4—881no—
437D4—881no—
438D4—881no—
439D4—881no—
440D4—881no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—112no—
447C2×C4—112no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4C4×D4411yescharacteristic
466C2×C4#6693511yescharacteristic
467C2×C4#6693711yescharacteristic
468C2×C4#6694611yescharacteristic
469C2×C4#6694711yescharacteristic
470C2×C4#6694811yescharacteristic
471C2×C4D8×D1111yescharacteristic
472C2×C4#6696411yescharacteristic
473C2×C4SD16×D1111yescharacteristic
474C2×C4#6696711yescharacteristic
475C2×C4#6696711yescharacteristic
476C2×C4#6696711yescharacteristic
477C2×C4#6697111yescharacteristic
478C2×C4#6697111yescharacteristic
479C8—42no—
480C8—81no—
481C8—442no—
482C8—881no—
483C22—222no—
484C22—222no—
485C22—222no—
486C22—441no—
487C22—441no—
488C22—441no—
489C22—441no—
490C22—882no—
491C22—882no—
492C22—882no—
493C22—882no—
494C22—882no—
495C22—882no—
496C22—882no—
497C22#1062227811yescharacteristic
498C22D11×#10011yescharacteristic
499C22#1062236411yescharacteristic
500C22D11×#10211yescharacteristic
501C22#1062238311yescharacteristic
502C22#1062241611yescharacteristic
503C22#1062241611yescharacteristic
504C4—21no—
505C4—21no—
506C4—82no—
507C4—222no—
508C4—222no—
509C4—441no—
510C4#1062238611yescharacteristic
511C4#1062239511yescharacteristic
512C4#1062241911yescharacteristic
513C4#1062242511yescharacteristic
514C4#1062247611yescharacteristic
515C4#1062247811yescharacteristic
516C4#1062249511yescharacteristic
517C4#1062249911yescharacteristic
518C2—442no—
519C2—1762no—
520C2#1306728211yescharacteristic
521C2#1306729211yescharacteristic
522C2#1306733711yescharacteristic
523C2#1306735011yescharacteristic
524C2#1306893211yescharacteristic
525C2#1306905311yescharacteristic
526C2#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#9141
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×#10622450C2semidirect
3. #13068593C2semidirect
4. C2×#10622123C2semidirect
5. C2×#10622123C2semidirect
6. #13066499C2semidirect
7. C11×#1296C2semidirect
69. C11×C4⋊C8D4semidirect
75. C4⋊(C11⋊C8)D4semidirect
158. #1296D11semidirect
328. C4⋊C8D44semidirect
414. C11#9141semidirect

Maximal subgroups

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

subgroupindex
C2×#106224502
#130769622
#130685932
C2×#106221232
#130664992
C11×#12962
#914111