Finite Group Databasebeta

← #14657140

Subgroups — #14657140

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#13073558C211yesmaximal, characteristic
2#13069421C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic, complemented
4C2×#10622123C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6#13066457C211yesmaximal, characteristic, complemented
7C11×#1948C211yesmaximal, characteristic, complemented
8C2×#66948—21no—
9C2×#66948—21no—
10C2×#66927—21no—
11C2×#66927C2211yescharacteristic
12C2×C4×D44C2211yescharacteristic
13C2×C11×#106—21no—
14C2×C11×C4⋊C8C2211yescharacteristic
15C11×#384C2211yescharacteristic
16C4×C11×C4⋊C4C2211yescharacteristic
17C2×#66873—21no—
18C2×#66873—22no—
19#10622552—21no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622284—22no—
23C11×#340—21no—
24#10622167—21no—
25#10622123—22no—
26#10622121—22no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—22no—
30C22×D44—22no—
31C22×D44D411yescharacteristic
32C22×D44D412yes—
33C22×C4×D11—21no—
34C22×C8×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48#66948—42no—
49#66948—42no—
50#66948—42no—
51#66948—42no—
52#66927—21no—
53#66927—21no—
54#66927—21no—
55#66927—21no—
56#66927—42no—
57#66927—42no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C11×#106—42no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yescomplemented
65C11×#95—21no—
66#66873—44no—
67#66873—42no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10409—111nomaximal, Sylow
73C23×D11—21no—
74C23×D11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C2×D44—21no—
83C2×D44—22no—
84C2×D44—21no—
85C2×D44—22no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—44no—
90C2×D44—44no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—44no—
94C2×D44—44no—
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×D44—41no—
106C2×D44—41no—
107C2×D44—82no—
108C2×D44—82no—
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—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4D812yes—
127C11×C4⋊C4SD1612yes—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11#4111yescharacteristic
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146#2541—111no—
147#1957—111no—
148#1948D1111yescharacteristic, complemented
149#1802—111no—
150C2×#331—111no—
151C2×D4⋊C8—111no—
152#1279—111no—
153C23×C11#12011yescharacteristic
154C22×D11—22no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—42no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—42no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12311yescharacteristic
183C2×C4×C11#12311yescharacteristic
184C2×C4×C11#12411yescharacteristic
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C2×SD1611yescharacteristic
187C2×C4×C11C2×SD1611yescharacteristic
188C2×C4×C11#13511yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196D44—22no—
197D44—22no—
198D44—44no—
199D44—41no—
200D44—41no—
201D44—82no—
202D44—88no—
203D44—88no—
204D44—81no—
205D44—81no—
206D44—81no—
207D44—81no—
208D44—81no—
209D44—81no—
210D44—81no—
211D44—81no—
212C4×D11—81no—
213C4×D11—81no—
214C4×D11—81no—
215C4×D11—81no—
216C8×C11—42no—
217C11⋊C8—42no—
218C11⋊C8—81no—
219C2×#127—111no—
220C2×#127—221no—
221C2×#121—221no—
222C2×#121—221no—
223C2×C4×D4—111no—
224C2×#106—21no—
225C2×C4⋊C8—111no—
226C2×C4⋊C8C2×D1111yescharacteristic
227C2×#102—221no—
228C2×#102—222no—
229C2×C4×C8—111no—
230#392—222no—
231#390—221no—
232#384C2×D1111yescharacteristic
233C4×C4⋊C4C2×D1111yescharacteristic
234#340—21no—
235#340—221no—
236#331—222no—
237D4⋊C8—222no—
238C22×C11#39411yescharacteristic
239C22×C11#44711yescharacteristic
240C22×C11#44911yescharacteristic
241C22×C11#45011yescharacteristic
242C22×C11#45011yescharacteristic
243C22×C11#45311yescharacteristic
244C22×C11#45511yescharacteristic
245C2×D11—42no—
246C2×D11—42no—
247C2×D11—42no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C2×D11—82no—
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—82no—
256C2×D11—82no—
257C2×D11—82no—
258C2×D11—82no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—161no—
264C4×C11#45911yescharacteristic
265C4×C11#46011yescharacteristic
266C4×C11#46511yescharacteristic
267C4×C11#46911yescharacteristic
268C4×C11#48111yescharacteristic
269C4×C11#48211yescharacteristic
270C4×C11#48611yescharacteristic
271C4×C11#49011yescharacteristic
272Dic11—81no—
273C22×D4—111no—
274C22×D4—112no—
275C22×D4—222no—
276C22×D4—222no—
277C22×D4—221no—
278C22×D4—221no—
279C23×C4—221no—
280C22×C8—21no—
281C22×C8—221no—
282C22×C8—221no—
283#127—221no—
284#127—221no—
285#127—221no—
286#127—221no—
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—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4C22⋊D1111yescharacteristic
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—221no—
306C2×C42—21no—
307C2×C42C22×D1111yescharacteristic
308#106—42no—
309C4⋊C8—21no—
310C4⋊C8—221no—
311C4⋊C8—221no—
312C4⋊C8D4412yescomplemented
313#102—444no—
314#102—442no—
315C4×C8—221no—
316C4×C8—221no—
317#95—21no—
318C2×C11#162111yescharacteristic
319C2×C11#162911yescharacteristic
320C2×C11#163911yescharacteristic
321C2×C11#164211yescharacteristic
322C2×C11#203411yescharacteristic
323C2×C11#203711yescharacteristic
324C2×C11#204111yescharacteristic
325D11—82no—
326D11—162no—
327C24—221no—
328C24—222no—
329C2×D4—112no—
330C2×D4—221no—
331C2×D4—222no—
332C2×D4—221no—
333C2×D4—222no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—442no—
338C2×D4—442no—
339C2×D4—444no—
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—
355C2×D4—882no—
356C2×D4—882no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4—221no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4D4×D1111yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C2×C8—22no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—222no—
374C2×C8—441no—
375C2×C8—441no—
376C2×C8—441no—
377C2×C8—441no—
378C2×C8—441no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—42no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4#432312yes—
389C4⋊C4#432512yes—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C42—41no—
395C42—41no—
396C42C2×D4411yescharacteristic
397C42#433911yescharacteristic
398C42#434311yescharacteristic
399C42#434311yescharacteristic
400C11#1040911yescharacteristic, complemented, Sylow
401C23—222no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—442no—
409C23—442no—
410C23—442no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23—442no—
415C23#6699011yescharacteristic
416D4—222no—
417D4—222no—
418D4—444no—
419D4—441no—
420D4—441no—
421D4—882no—
422D4—888no—
423D4—888no—
424D4—881no—
425D4—881no—
426D4—881no—
427D4—881no—
428D4—881no—
429D4—881no—
430D4—881no—
431D4—881no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—881no—
447C2×C4—881no—
448C2×C4—881no—
449C2×C4—881no—
450C2×C4#6694711yescharacteristic
451C2×C4#6694711yescharacteristic
452C2×C4#6694811yescharacteristic
453C2×C4#6694811yescharacteristic
454C2×C4SD16×D1111yescharacteristic
455C2×C4#6696711yescharacteristic
456C2×C4#6696711yescharacteristic
457C2×C4#6696911yescharacteristic
458C2×C4#6698311yescharacteristic
459C2×C4C2×#432311yescharacteristic
460C2×C4C2×#432511yescharacteristic
461C2×C4#6700011yescharacteristic
462C2×C4#6700211yescharacteristic
463C2×C4#6700211yescharacteristic
464C8—42no—
465C8—442no—
466C8—881no—
467C22—442no—
468C22—442no—
469C22—442no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22—882no—
478C22—882no—
479C22—882no—
480C22—882no—
481C22#1062260411yescharacteristic
482C22#1062264911yescharacteristic
483C22#1062265911yescharacteristic
484C22#1062278211yescharacteristic
485C22#1062278511yescharacteristic
486C22#1062281111yescharacteristic
487C22#1062281511yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—161no—
493C4—881no—
494C4#1062247611yescharacteristic
495C4#1062247711yescharacteristic
496C4#1062247811yescharacteristic
497C4#1062247911yescharacteristic
498C4#1062262811yescharacteristic
499C4#1062264011yescharacteristic
500C4#1062268011yescharacteristic
501C4#1062270111yescharacteristic
502C2—882no—
503C2—1762no—
504C2#1306767911yescharacteristic
505C2#1306773111yescharacteristic
506C2#1306779311yescharacteristic
507C2#1306781511yescharacteristic
508C2#1306980711yescharacteristic
509C2#1306982811yescharacteristic
510C2#1306985011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1948C2
socleC23×C11#120
prime radical#13073558C2
hypercenter#1948D11
hypocenterC11#10409
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #13069421C2semidirect
3. #13068613C2semidirect
4. C2×#10622123C2semidirect
5. C2×#10622121C2semidirect
6. #13066457C2semidirect
7. C11×#1948C2semidirect
64. C11×C4⋊C8D4semidirect
148. #1948D11semidirect
312. C4⋊C8D44semidirect
400. C11#10409semidirect

Maximal subgroups

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

subgroupindex
#130735582
#130694212
#130686132
C2×#106221232
C2×#106221212
#130664572
C11×#19482
#1040911