Finite Group Databasebeta

← #14657137

Subgroups — #14657137

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073563C211yesmaximal, characteristic
2#13069423C211yesmaximal, characteristic, complemented
3#13069380C211yesmaximal, characteristic, complemented
4#13068617C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×#66993—21no—
10C2×#66991—21no—
11C2×#66991—21no—
12C2×C4×D44C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15#10622836—22no—
16#10622834—21no—
17C2×#66896—22no—
18C2×#66885—21no—
19C2×#66881—21no—
20#10622548C2211yescharacteristic
21C4×C4⋊Dic11C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#331—22no—
24#10622189—21no—
25#10622189—21no—
26#10622121—22no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11D412yes—
30C22×C22⋊D11—22no—
31C22×C22⋊D11—22no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—22no—
42C2×C22⋊Dic11—22no—
43#66993—42no—
44#66993—42no—
45#66991—42no—
46#66991—42no—
47#66991—42no—
48#66991—42no—
49C2×(C2×D11)⋊C4—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D411yescharacteristic
55C2×C4⋊Dic11D411yescharacteristic
56C2×C4×Dic11—21no—
57C22×C11⋊C8—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yescomplemented
66#66896—44no—
67C11⋊#95—21no—
68#66885—42no—
69#66881—42no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10409—111nomaximal, Sylow
73C24×C11—22no—
74C23×D11—21no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
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—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—44no—
95C2×C22⋊D11—44no—
96C2×C22⋊D11—44no—
97C2×C22⋊D11—44no—
98C2×C22⋊D11—82no—
99C2×C22⋊D11—82no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—41no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44SD1612yes—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C4×D11—41no—
115C2×C4×D11—41no—
116C2×C8×C11—22no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11#4111yescharacteristic
125C42×C11#4111yescharacteristic
126C22⋊Dic11—44no—
127C22⋊Dic11—44no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—42no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138C4⋊Dic11—41no—
139C4⋊Dic11D812yes—
140C4⋊Dic11SD1612yes—
141C4×Dic11—41no—
142C4×Dic11—41no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146#2541—111no—
147#1957—111no—
148#1948—111no—
149#1802—111no—
150C2×#331D1111yescharacteristic, complemented
151C2×D4⋊C8—111no—
152#1279—111no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11#12011yescharacteristic
161C22×D11—22no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168D4×C11—44no—
169D4×C11—82no—
170D4×C11—81no—
171D4×C11—81no—
172D4×C11—81no—
173D4×C11—81no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177D4×C11—81no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12311yescharacteristic
184C2×C4×C11#12311yescharacteristic
185C2×C4×C11#12411yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11C2×SD1611yescharacteristic
188C2×C4×C11C2×SD1611yescharacteristic
189C2×C4×C11#13511yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C22⋊D11—88no—
195C22⋊D11—88no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208D44—22no—
209D44—22no—
210D44—41no—
211D44—41no—
212C4×D11—81no—
213C4×D11—81no—
214C4×D11—81no—
215C4×D11—81no—
216C8×C11—42no—
217C8×C11—81no—
218C11⋊C8—42no—
219C2×#127—221no—
220C2×#127C2×D1111yescharacteristic
221C2×#121—221no—
222C2×#121—221no—
223C2×C4×D4—111no—
224C2×#106—221no—
225C2×C4⋊C8C2×D1111yescharacteristic
226C2×C4⋊C8C2×D1111yescharacteristic
227C2×#102—221no—
228C2×#102—222no—
229C2×C4×C8—111no—
230#392—222no—
231#390—221no—
232#384—111no—
233C4×C4⋊C4—111no—
234#340—221no—
235#340—221no—
236#331—22no—
237D4⋊C8—222no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11#39411yescharacteristic
246C22×C11#44711yescharacteristic
247C22×C11#44911yescharacteristic
248C22×C11#45011yescharacteristic
249C22×C11#45011yescharacteristic
250C22×C11#45311yescharacteristic
251C22×C11#45511yescharacteristic
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11#45911yescharacteristic
262C4×C11#46011yescharacteristic
263C4×C11#46511yescharacteristic
264C4×C11#46911yescharacteristic
265C4×C11#48111yescharacteristic
266C4×C11#48211yescharacteristic
267C4×C11#48611yescharacteristic
268C4×C11#49011yescharacteristic
269Dic11—42no—
270Dic11—42no—
271Dic11—81no—
272Dic11—161no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—111no—
276C22×D4—222no—
277C22×D4—222no—
278C22×D4D4412yes—
279C23×C4—221no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—221no—
283#127—21no—
284#127—21no—
285#127—21no—
286#127—21no—
287#127—442no—
288#127—442no—
289#121—442no—
290#121—442no—
291#121—442no—
292#121—442no—
293C4×D4—221no—
294C4×D4—221no—
295C4×D4—221no—
296C4×D4—221no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—221no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308#106—442no—
309C4⋊C8—21no—
310C4⋊C8—21no—
311C4⋊C8—21no—
312C4⋊C8C22⋊D1112yescomplemented
313#102—442no—
314#102—444no—
315C4×C8—221no—
316C4×C8—221no—
317#95—221no—
318C2×C11—162no—
319C2×C11#162111yescharacteristic
320C2×C11#162911yescharacteristic
321C2×C11#163911yescharacteristic
322C2×C11#164211yescharacteristic
323C2×C11#203411yescharacteristic
324C2×C11#203711yescharacteristic
325C2×C11#204111yescharacteristic
326D11—82no—
327C24—22no—
328C24—221no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—112no—
346C2×D4—221no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C2×D4—444no—
352C2×D4—444no—
353C2×D4—444no—
354C2×D4—444no—
355C2×D4—882no—
356C2×D4—882no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4C2×D4411yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4D4×D1111yescharacteristic
370C2×C8—22no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—222no—
377C2×C8—441no—
378C2×C8—441no—
379C4⋊C4—112no—
380C4⋊C4—112no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—442no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C42—441no—
395C42—441no—
396C42#433911yescharacteristic
397C42#434111yescharacteristic
398C42#434111yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C11#1040911yescharacteristic, complemented, Sylow
401C23—42no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—222no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23#6693511yescharacteristic
416D4—44no—
417D4—82no—
418D4—81no—
419D4—81no—
420D4—81no—
421D4—81no—
422D4—81no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—222no—
427D4—222no—
428D4—441no—
429D4—441no—
430D4—888no—
431D4—888no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4—881no—
448C2×C4—881no—
449C2×C4—881no—
450C2×C4#6693611yescharacteristic
451C2×C4#6693811yescharacteristic
452C2×C4#6693911yescharacteristic
453C2×C4D8×D1111yescharacteristic
454C2×C4#6696411yescharacteristic
455C2×C4#6696411yescharacteristic
456C2×C4#6696411yescharacteristic
457C2×C4SD16×D1111yescharacteristic
458C2×C4SD16×D1111yescharacteristic
459C2×C4#6696711yescharacteristic
460C2×C4#6696911yescharacteristic
461C2×C4#6698311yescharacteristic
462C2×C4#6699111yescharacteristic
463C2×C4#6699211yescharacteristic
464C8—42no—
465C8—81no—
466C8—442no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—82no—
473C22—82no—
474C22—442no—
475C22—442no—
476C22—442no—
477C22—881no—
478C22—881no—
479C22—881no—
480C22—881no—
481C22#1062235911yescharacteristic
482C22#1062236011yescharacteristic
483C22#1062238611yescharacteristic
484C22#1062238911yescharacteristic
485C22#1062238911yescharacteristic
486C22#1062239411yescharacteristic
487C22#1062257411yescharacteristic
488C4—21no—
489C4—21no—
490C4—442no—
491C4—442no—
492C4—881no—
493C4—1761no—
494C4#1062237311yescharacteristic
495C4#1062237711yescharacteristic
496C4#1062239011yescharacteristic
497C4#1062239211yescharacteristic
498C4#1062276311yescharacteristic
499C4#1062277211yescharacteristic
500C4#1062277611yescharacteristic
501C4#1062278411yescharacteristic
502C2—162no—
503C2—882no—
504C2#1306768211yescharacteristic
505C2#1306773311yescharacteristic
506C2#1306779611yescharacteristic
507C2#1306781711yescharacteristic
508C2#1306980411yescharacteristic
509C2#1306982711yescharacteristic
510C2#1306984911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11#120
prime radical#13073563C2
hypercenterC2×#331D11
hypocenterC11#10409
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #13069423C2semidirect
3. #13069380C2semidirect
4. #13068617C2semidirect
5. C2×#10622121C2semidirect
6. #13066455C2semidirect
7. C2×C11×#331C2semidirect
65. C11×C4⋊C8D4semidirect
150. C2×#331D11semidirect
312. C4⋊C8C22⋊D11semidirect
400. C11#10409semidirect

Maximal subgroups

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

subgroupindex
#130735632
#130694232
#130693802
#130686172
C2×#106221212
#130664552
C2×C11×#3312
#1040911