Finite Group Databasebeta

← #14657135

Subgroups — #14657135

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#13069423C211yesmaximal, characteristic, complemented
2#13069379C211yesmaximal, characteristic, complemented
3#13068616C211yesmaximal, characteristic, complemented
4C2×#10622182C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#13066457C211yesmaximal, characteristic, complemented
7C11×#2541C211yesmaximal, characteristic
8C2×C11×#127—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C11×#121—21no—
11C2×C11×#121—21no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#392—22no—
14C11×#390—21no—
15C4×C11×C4⋊C4C2211yescharacteristic
16C2×#66896—21no—
17C2×#66896—22no—
18C2×#66872—21no—
19#10622548C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622182—22no—
24D4⋊(C11⋊C8)—22no—
25#10622167—21no—
26#10622167—21no—
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D411yescharacteristic
32C22×D4×C11D412yes—
33C23×C4×C11—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—42no—
39C11×#127—42no—
40C11×#121—42no—
41C11×#121—42no—
42C11×#121—42no—
43C11×#121—42no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—21no—
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8—21no—
62C11×#95—21no—
63#66896—44no—
64#66896—42no—
65#66872—42no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yescomplemented
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10409—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11—22no—
75C2×D4×C11—21no—
76C2×D4×C11—22no—
77C2×D4×C11—21no—
78C2×D4×C11—22no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—44no—
85C2×D4×C11—44no—
86C2×D4×C11—44no—
87C2×D4×C11—44no—
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—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—82no—
101C2×D4×C11—82no—
102C2×D4×C11SD1612yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×Dic11—41no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4D812yes—
121C11×C4⋊C4SD1612yes—
122C11×C22⋊C4—44no—
123C11×C22⋊C4—44no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11#4111yescharacteristic
132C4⋊Dic11—42no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146#2541D1111yescharacteristic
147#1957—111no—
148#1948—111no—
149#1802—111no—
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—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11#12011yescharacteristic
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—44no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—82no—
174D4×C11—88no—
175D4×C11—88no—
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×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11—81no—
198C2×C4×C11—81no—
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12311yescharacteristic
203C2×C4×C11#12311yescharacteristic
204C2×C4×C11#12411yescharacteristic
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×SD1611yescharacteristic
207C2×C4×C11C2×SD1611yescharacteristic
208C2×C4×C11#13511yescharacteristic
209C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
213C2×Dic11—81no—
214C2×Dic11—81no—
215C2×Dic11—81no—
216C11⋊C8—42no—
217C11⋊C8—42no—
218C11⋊C8—81no—
219C2×#127—21no—
220C2×#127C2×D1111yescharacteristic
221C2×#121—21no—
222C2×#121—21no—
223C2×C4×D4C2×D1111yescharacteristic
224C2×#106—221no—
225C2×C4⋊C8—111no—
226C2×C4⋊C8—111no—
227C2×#102—221no—
228C2×#102—222no—
229C2×C4×C8—111no—
230#392—22no—
231#390—21no—
232#384—111no—
233C4×C4⋊C4C2×D1111yescharacteristic
234#340—221no—
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—82no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11#39411yescharacteristic
253C22×C11#44711yescharacteristic
254C22×C11#44911yescharacteristic
255C22×C11#45011yescharacteristic
256C22×C11#45011yescharacteristic
257C22×C11#45311yescharacteristic
258C22×C11#45511yescharacteristic
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—81no—
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—161no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4C22⋊D1111yescharacteristic
278C22×D4C22⋊D1112yes—
279C23×C4—21no—
280C22×C8—221no—
281C22×C8—221no—
282C22×C8—221no—
283#127—21no—
284#127—21no—
285#127—21no—
286#127—21no—
287#127—42no—
288#127—42no—
289#121—42no—
290#121—42no—
291#121—42no—
292#121—42no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—21no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4C22⋊D1111yescharacteristic
301C2×C4⋊C4C22⋊D1111yescharacteristic
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—21no—
306C2×C42—21no—
307C2×C42C22×D1111yescharacteristic
308#106—442no—
309C4⋊C8—112no—
310C4⋊C8—221no—
311C4⋊C8—221no—
312C4⋊C8—221no—
313#102—444no—
314#102—442no—
315C4×C8—221no—
316C4×C8—221no—
317#95—21no—
318C2×C11—82no—
319C2×C11—162no—
320C2×C11#162111yescharacteristic
321C2×C11#162911yescharacteristic
322C2×C11#163911yescharacteristic
323C2×C11#164211yescharacteristic
324C2×C11#203411yescharacteristic
325C2×C11#203711yescharacteristic
326C2×C11#204111yescharacteristic
327C24—21no—
328C24—22no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
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—82no—
355C2×D4—82no—
356C2×D4#432412yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—441no—
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C2×C8—222no—
371C2×C8—222no—
372C2×C8—441no—
373C2×C8—441no—
374C2×C8—441no—
375C2×C8—441no—
376C2×C8—441no—
377C2×C8—441no—
378C2×C8—441no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—442no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4#432312yes—
389C4⋊C4#432412yes—
390C22⋊C4—44no—
391C22⋊C4—44no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C42—41no—
395C42—41no—
396C42D4×D1111yescharacteristic
397C42#434111yescharacteristic
398C42#434111yescharacteristic
399C42#434111yescharacteristic
400C11#1040911yescharacteristic, complemented, Sylow
401C23—22no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23#6700611yescharacteristic
416D4—22no—
417D4—22no—
418D4—44no—
419D4—41no—
420D4—41no—
421D4—82no—
422D4—88no—
423D4—88no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
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—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—881no—
448C2×C4—881no—
449C2×C4—881no—
450C2×C4C2×#432311yescharacteristic
451C2×C4#6698511yescharacteristic
452C2×C4#6698511yescharacteristic
453C2×C4#6698511yescharacteristic
454C2×C4C2×#432411yescharacteristic
455C2×C4C2×#432411yescharacteristic
456C2×C4#6698811yescharacteristic
457C2×C4#6698811yescharacteristic
458C2×C4#6698911yescharacteristic
459C2×C4#6699111yescharacteristic
460C2×C4#6699211yescharacteristic
461C2×C4#6699211yescharacteristic
462C2×C4#6700211yescharacteristic
463C2×C4#6700311yescharacteristic
464C8—442no—
465C8—442no—
466C8—881no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22#1062283011yescharacteristic
482C22#1062283111yescharacteristic
483C22#1062283111yescharacteristic
484C22#1062283511yescharacteristic
485C22#1062285111yescharacteristic
486C22#1062285411yescharacteristic
487C22#1062285511yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—81no—
493C4—1761no—
494C4#1062264711yescharacteristic
495C4#1062264811yescharacteristic
496C4#1062265211yescharacteristic
497C4#1062265411yescharacteristic
498C4#1062268311yescharacteristic
499C4#1062268411yescharacteristic
500C4#1062268511yescharacteristic
501C4#1062268811yescharacteristic
502C2—82no—
503C2—162no—
504C2#1306768111yescharacteristic
505C2#1306773211yescharacteristic
506C2#1306779511yescharacteristic
507C2#1306781611yescharacteristic
508C2#1306980211yescharacteristic
509C2#1306982311yescharacteristic
510C2#1306984711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2541C2
socleC23×C11#120
hypercenter#2541D11
hypocenterC11#10409
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #13069423C2semidirect
2. #13069379C2semidirect
3. #13068616C2semidirect
4. C2×#10622182C2semidirect
5. C2×D4⋊(C11⋊C8)C2semidirect
6. #13066457C2semidirect
69. C4⋊(C11⋊C8)D4semidirect
400. C11#10409semidirect

Maximal subgroups

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

subgroupindex
#130694232
#130693792
#130686162
C2×#106221822
C2×D4⋊(C11⋊C8)2
#130664572
C11×#25412
#1040911