Finite Group Databasebeta

← #14657138

Subgroups — #14657138

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#13073562C211yesmaximal, characteristic
2#13069421C211yesmaximal, characteristic, complemented
3#13069377C211yesmaximal, characteristic, complemented
4C2×#10622123C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C11×#1802C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66993—21no—
10C2×#66983—21no—
11C2×#66983—21no—
12C2×#66927C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#102—21no—
15C11×#384C2211yescharacteristic
16#10622601—21no—
17C2×#66873—22no—
18C2×#66872—21no—
19#10622573—22no—
20C4×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#340—21no—
24D4⋊(C11⋊C8)—22no—
25#10622167—21no—
26#10622123—22no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C22×C22⋊D11—22no—
30C22×C22⋊D11—22no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44D412yes—
34C22×C8×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C42×C11C2311yescharacteristic
45#66993—42no—
46#66993—42no—
47#66983—42no—
48#66983—42no—
49#66983—42no—
50#66983—42no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D411yescharacteristic
55C2×C4×Dic11—21no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8—21no—
58#66927—21no—
59#66927—21no—
60#66927—21no—
61#66927—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×#102—42no—
65C11⋊#95—21no—
66#66873—44no—
67#66872—42no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yescomplemented
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10409—111nomaximal, Sylow
73C24×C11—21no—
74C23×D11—22no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11SD1612yes—
81C22×C4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C2×C22⋊D11—44no—
93C2×C22⋊D11—44no—
94C2×C22⋊D11—44no—
95C2×C22⋊D11—44no—
96C2×C22⋊D11—82no—
97C2×C22⋊D11—82no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—42no—
103C2×D44—42no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—41no—
116C2×C8×C11—41no—
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×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11#4111yescharacteristic
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—44no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11D812yes—
137C4⋊Dic11SD1612yes—
138C4×Dic11—41no—
139C4×Dic11—41no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146#2541—111no—
147#1957—111no—
148#1948—111no—
149#1802D1111yescharacteristic, complemented
150C2×#331—111no—
151C2×D4⋊C8—111no—
152#1279—111no—
153C23×C11—22no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11#12011yescharacteristic
161C22×D11—42no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—42no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—41no—
171D4×C11—41no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12311yescharacteristic
188C2×C4×C11#12311yescharacteristic
189C2×C4×C11#12411yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11C2×SD1611yescharacteristic
192C2×C4×C11C2×SD1611yescharacteristic
193C2×C4×C11#13511yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
198C22⋊D11—88no—
199C22⋊D11—88no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206D44—44no—
207D44—82no—
208D44—81no—
209D44—81no—
210D44—81no—
211D44—81no—
212D44—81no—
213D44—81no—
214D44—81no—
215D44—81no—
216C8×C11—81no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219C2×#127—111no—
220C2×#127—221no—
221C2×#121—221no—
222C2×#121—221no—
223C2×C4×D4C2×D1111yescharacteristic
224C2×#106—221no—
225C2×C4⋊C8—111no—
226C2×C4⋊C8C2×D1111yescharacteristic
227C2×#102—21no—
228C2×#102—222no—
229C2×C4×C8—111no—
230#392—222no—
231#390—221no—
232#384C2×D1111yescharacteristic
233C4×C4⋊C4—111no—
234#340—21no—
235#340—221no—
236#331—222no—
237D4⋊C8—222no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11#39411yescharacteristic
246C22×C11#44711yescharacteristic
247C22×C11#44911yescharacteristic
248C22×C11#45011yescharacteristic
249C22×C11#45011yescharacteristic
250C22×C11#45311yescharacteristic
251C22×C11#45511yescharacteristic
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—81no—
262C4×C11—161no—
263C4×C11#45911yescharacteristic
264C4×C11#46011yescharacteristic
265C4×C11#46511yescharacteristic
266C4×C11#46911yescharacteristic
267C4×C11#48111yescharacteristic
268C4×C11#48211yescharacteristic
269C4×C11#48611yescharacteristic
270C4×C11#49011yescharacteristic
271Dic11—42no—
272Dic11—42no—
273C22×D4—112no—
274C22×D4—222no—
275C22×D4—222no—
276C22×D4—221no—
277C22×D4—221no—
278C22×D4C22⋊D1111yescharacteristic
279C23×C4—21no—
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—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308#106—442no—
309C4⋊C8—21no—
310C4⋊C8—21no—
311C4⋊C8—112no—
312C4⋊C8—221no—
313#102—42no—
314#102—444no—
315C4×C8—221no—
316C4×C8—221no—
317#95—221no—
318C2×C11—82no—
319C2×C11#162111yescharacteristic
320C2×C11#162911yescharacteristic
321C2×C11#163911yescharacteristic
322C2×C11#164211yescharacteristic
323C2×C11#203411yescharacteristic
324C2×C11#203711yescharacteristic
325C2×C11#204111yescharacteristic
326D11—162no—
327C24—21no—
328C24—222no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—222no—
335C2×D4—222no—
336C2×D4—442no—
337C2×D4—442no—
338C2×D4—444no—
339C2×D4—444no—
340C2×D4—444no—
341C2×D4—444no—
342C2×D4—441no—
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—882no—
355C2×D4—882no—
356C2×D4#432512yes—
357C22×C4—21no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4D4×D1111yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—222no—
374C2×C8—222no—
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—112no—
387C4⋊C4—112no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—444no—
393C22⋊C4—444no—
394C42—441no—
395C42—441no—
396C42#433911yescharacteristic
397C42#433911yescharacteristic
398C42D4×D1111yescharacteristic
399C42#434111yescharacteristic
400C11#1040911yescharacteristic, complemented, Sylow
401C23—22no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—442no—
409C23—442no—
410C23—442no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23—442no—
415C23#6699011yescharacteristic
416D4—22no—
417D4—22no—
418D4—41no—
419D4—41no—
420D4—444no—
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—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4#6693611yescharacteristic
451C2×C4#6693711yescharacteristic
452C2×C4#6693711yescharacteristic
453C2×C4#6693811yescharacteristic
454C2×C4D8×D1111yescharacteristic
455C2×C4#6696411yescharacteristic
456C2×C4SD16×D1111yescharacteristic
457C2×C4#6696711yescharacteristic
458C2×C4#6698211yescharacteristic
459C2×C4#6698511yescharacteristic
460C2×C4#6699211yescharacteristic
461C2×C4C2×#432511yescharacteristic
462C2×C4#6700211yescharacteristic
463C2×C4#6700311yescharacteristic
464C8—81no—
465C8—442no—
466C8—442no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22—882no—
478C22—882no—
479C22—882no—
480C22—882no—
481C22#1062257211yescharacteristic
482C22#1062265011yescharacteristic
483C22#1062265911yescharacteristic
484C22#1062276911yescharacteristic
485C22#1062278211yescharacteristic
486C22#1062281111yescharacteristic
487C22#1062281511yescharacteristic
488C4—21no—
489C4—21no—
490C4—81no—
491C4—161no—
492C4—442no—
493C4—442no—
494C4#1062237311yescharacteristic
495C4#1062237511yescharacteristic
496C4#1062237711yescharacteristic
497C4#1062239911yescharacteristic
498C4#1062258111yescharacteristic
499C4#1062261611yescharacteristic
500C4#1062265211yescharacteristic
501C4#1062266111yescharacteristic
502C2—82no—
503C2—1762no—
504C2#1306768011yescharacteristic
505C2#1306773111yescharacteristic
506C2#1306779411yescharacteristic
507C2#1306781411yescharacteristic
508C2#1306980511yescharacteristic
509C2#1306982411yescharacteristic
510C2#1306984811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1802C2
socleC23×C11#120
prime radical#13073562C2
hypercenter#1802D11
hypocenterC11#10409
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #13069421C2semidirect
3. #13069377C2semidirect
4. C2×#10622123C2semidirect
5. C2×D4⋊(C11⋊C8)C2semidirect
6. #13066455C2semidirect
7. C11×#1802C2semidirect
69. C4⋊(C11⋊C8)D4semidirect
149. #1802D11semidirect
400. C11#10409semidirect

Maximal subgroups

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

subgroupindex
#130735622
#130694212
#130693772
C2×#106221232
C2×D4⋊(C11⋊C8)2
#130664552
C11×#18022
#1040911