Finite Group Databasebeta

← #14652766

Subgroups — #14652766

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068378C211yesmaximal, characteristic, complemented
2C2×#10622176C212yesmaximal, complemented
3C2×#10622175C212yesmaximal
4#13066846C211yesmaximal, characteristic, complemented
5C11×#2850C211yesmaximal, characteristic
6C2×C11×#124C411yescharacteristic, complemented
7C2×C11×C22⋊Q8C2211yescharacteristic
8C2×C11×#121C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11—21no—
11C11×#391C411yescharacteristic, complemented
12C11×#390C411yescharacteristic, complemented
13C11×#388—21no—
14C11×#388—21no—
15C11×#386—21no—
16C11×#386—21no—
17C11×#382C411yescharacteristic, complemented
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×#66867—21no—
22#10622176—24no—
23#10622175—24no—
24#10622162—21no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—22no—
32C11×#124—42no—
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—22no—
35C11×#121—22no—
36C11×#121—22no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C42×C11—42no—
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11—42no—
53C2×C4⋊Dic11—42no—
54C22×C11⋊C8—22no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—42no—
62C22⋊(C11⋊C8)—22no—
63C22⋊(C11⋊C8)D414yes—
64#66867—42no—
65#9682—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×D4×C11—22no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C22⋊C411yescharacteristic
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22⋊C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11#4112yes—
101C22×Dic11—24no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C22×Dic11—42no—
106C22×Dic11—42no—
107C22×Dic11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—42no—
118C42×C11—22no—
119C42×C11—22no—
120C42×C11—41no—
121C42×C11—41no—
122C4⋊Dic11—48no—
123C2×C11⋊C8—24no—
124C2×C11⋊C8—42no—
125C2×C11⋊C8—42no—
126#2850D1111yescharacteristic
127#1749—111no—
128C2×#328—112no—
129C2×#327—112no—
130C4⋊#95—111no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11#12411yescharacteristic
144C23×C11#12711yescharacteristic
145C23×C11AGL(1,ℤ/8)11yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147C23×C11#13711yescharacteristic
148C23×C11#13711yescharacteristic
149Q8×C11—82no—
150D4×C11—82no—
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154D4×C11—81no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11#9912yes—
185C2×C4×C11#10412yes—
186C2×C4×C11C4×D412yes—
187C2×C4×C11#12112yes—
188C2×Dic11—44no—
189C2×Dic11—44no—
190C2×Dic11—44no—
191C2×Dic11—82no—
192C2×Dic11—82no—
193C2×Dic11—82no—
194C2×Dic11—82no—
195C11⋊C8—44no—
196C2×#124Dic1111yescharacteristic, complemented
197C2×C22⋊Q8C2×D1111yescharacteristic
198C2×#121C2×D1111yescharacteristic
199C22×C4⋊C4—221no—
200C22×C42C2×D1111yescharacteristic
201C2×C22⋊C8—112no—
202C2×#97—221no—
203#391Dic1111yescharacteristic, complemented
204#390Dic1111yescharacteristic, complemented
205#388—21no—
206#388—21no—
207#386—21no—
208#386—21no—
209#382Dic1111yescharacteristic, complemented
210C2×#95—112no—
211C2×#95—221no—
212#336—221no—
213#328—224no—
214#327—224no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11#39011yescharacteristic
235C22×C11C2×#9911yescharacteristic
236C22×C11#41011yescharacteristic
237C22×C11#41711yescharacteristic
238C22×C11#41711yescharacteristic
239C22×C11C2×#10411yescharacteristic
240C22×C11#42111yescharacteristic
241C22×C11#48911yescharacteristic
242C22×C11#48911yescharacteristic
243C22×C11#49611yescharacteristic
244C22×C11#49711yescharacteristic
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—22no—
249C4×C11—41no—
250C4×C11—41no—
251C4×C11—81no—
252C4×C11—81no—
253C4×C11—81no—
254Dic11—84no—
255C22×Q8C2×Dic1111yescharacteristic
256C22×D4—21no—
257C22×D4C2×Dic1111yescharacteristic
258C23×C4—222no—
259C23×C4C22⋊D1111yescharacteristic
260C23×C4C22⋊D1111yescharacteristic
261C23×C4C22×D1111yescharacteristic
262C22×C8—222no—
263#124—42no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266#121—22no—
267#121—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—224no—
270C2×C4⋊C4—442no—
271C2×C4⋊C4—442no—
272C2×C4⋊C4C2×Dic1111yescharacteristic
273C2×C4⋊C4C2×Dic1111yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C42—42no—
281C2×C42C2×Dic1111yescharacteristic
282C2×C42C2×Dic1111yescharacteristic
283C2×C42C22⋊D1111yescharacteristic
284C2×C42C22⋊D1111yescharacteristic
285C22⋊C8—114no—
286C22⋊C8—222no—
287#97—442no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—222no—
293#95—222no—
294#95—442no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—161no—
300C2×C11#150411yescharacteristic
301C2×C11#150911yescharacteristic
302C2×C11#151211yescharacteristic
303C2×C11#151311yescharacteristic
304C2×C11#195911yescharacteristic
305C2×C11#196411yescharacteristic
306C2×C11#198011yescharacteristic
307C24—21no—
308C24C2×C22⋊D1111yescharacteristic
309C2×Q8—22no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—224no—
335C22×C4—442no—
336C22×C4—442no—
337C22×C4—442no—
338C22×C4—442no—
339C22×C4—442no—
340C22×C4—442no—
341C22×C4C22⋊Dic1111yescharacteristic
342C22×C4C22⋊Dic1111yescharacteristic
343C22×C4C22⋊Dic1111yescharacteristic
344C22×C4C22⋊Dic1111yescharacteristic
345C22×C4D4×D1112yes—
346C22×C4#434112yes—
347C22×C4C22×Dic1111yescharacteristic
348C22×C4C2×C22⋊D1111yescharacteristic
349C2×C8—224no—
350C2×C8—442no—
351C2×C8—442no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—42no—
355C4⋊C4—448no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C42—22no—
364C42—22no—
365C42—41no—
366C42—41no—
367C11#968211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23#6698911yescharacteristic
380C23#6699311yescharacteristic
381C23#6700211yescharacteristic
382C23#6700211yescharacteristic
383C23#6700411yescharacteristic
384C23#6700411yescharacteristic
385C23C2×C22⋊Dic1111yescharacteristic
386Q8—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—444no—
422C2×C4—444no—
423C2×C4—444no—
424C2×C4—882no—
425C2×C4—882no—
426C2×C4—882no—
427C2×C4—882no—
428C2×C4#6689812yes—
429C2×C4#6690112yes—
430C2×C4D4×Dic1112yes—
431C2×C4#6699112yes—
432C8—444no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#1062266811yescharacteristic
453C22#1062266811yescharacteristic
454C22#1062267111yescharacteristic
455C22#1062267311yescharacteristic
456C22C2×#6689811yescharacteristic
457C22#1062283411yescharacteristic
458C22#1062284511yescharacteristic
459C22#1062284511yescharacteristic
460C22C2×#6690111yescharacteristic
461C22#1062284911yescharacteristic
462C22#1062285311yescharacteristic
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4—884no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—161no—
478C2#1306712011yescharacteristic
479C2#1306714111yescharacteristic
480C2#1306715411yescharacteristic
481C2#1306715911yescharacteristic
482C2#1306943311yescharacteristic
483C2#1306945311yescharacteristic
484C2#1306953611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2850C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2850D11
hypocenterC11#9682
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. #13068378C2semidirect
2. C2×#10622176C2semidirect
4. #13066846C2semidirect
6. C2×C11×#124C4semidirect
11. C11×#391C4semidirect
12. C11×#390C4semidirect
17. C11×#382C4semidirect
196. C2×#124Dic11semidirect
203. #391Dic11semidirect
204. #390Dic11semidirect
209. #382Dic11semidirect
367. C11#9682semidirect

Maximal subgroups

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

subgroupindex
#130683782
C2×#106221762
C2×#106221752
#130668462
C11×#28502
#968211