Finite Group Databasebeta

← #14645349

Subgroups — #14645349

Order 2816.

794 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069411C211yesmaximal, characteristic, complemented
2#13068608C211yesmaximal, characteristic, complemented
3#13067306C211yesmaximal, characteristic, complemented
4#13067293C211yesmaximal, characteristic, complemented
5#13067071C211yesmaximal, characteristic, complemented
6#13067067C211yesmaximal, characteristic, complemented
7C11×#3506C211yesmaximal, characteristic
8C11×#559—22no—
9C11×#556—21no—
10C11×#555—21no—
11C11×#553—22no—
12C11×#550—21no—
13C11×#547—21no—
14C11×#538C414yes—
15C11×#535—21no—
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C11×#525—22no—
19C11×#520—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66897—21no—
22C2×C22⋊(C11⋊C8)—22no—
23#10622537C2211yescharacteristic
24#10622537C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622185—21no—
28#10622185—21no—
29#10622184—21no—
30#10622182—21no—
31Q8⋊(C11⋊C8)—22no—
32D4⋊(C11⋊C8)—22no—
33#10622168—21no—
34C2×C11×#41—22no—
35C2×C11×#41—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11D412yes—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×#127—22no—
42C11×#127D411yescharacteristic
43C11×#126—24no—
44C11×#125—21no—
45C11×#124—22no—
46C11×#124—24no—
47C11×#124—21no—
48C11×#123—24no—
49C11×#123—24no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8C2×C412yes—
53C11×#121—22no—
54C11×#121—22no—
55C11×#121—22no—
56C11×#121—24no—
57C11×#121—21no—
58C11×#121C2×C412yes—
59C11×#120—24no—
60C4×Q8×C11—22no—
61C4×Q8×C11—21no—
62C4×Q8×C11D412yes—
63C4×D4×C11—22no—
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11D412yes—
72C11×#117—22no—
73C11×#117—22no—
74C11×#117—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C22⋊C4C2×C412yes—
78C2×C42×C11C2311yescharacteristic
79C2×#4318—21no—
80C2×#4318—21no—
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83#66897—42no—
84C22⋊(C11⋊C8)—44no—
85C4⋊(C11⋊C8)—21no—
86C4⋊(C11⋊C8)—21no—
87C4⋊(C11⋊C8)—21no—
88C4⋊(C11⋊C8)—21no—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)—21no—
91C4×C11⋊C8—21no—
92C4×C11⋊C8—21no—
93#8358—111nomaximal, Sylow
94C24×C11C22⋊C412yes—
95C11×#41—41no—
96C11×#41—41no—
97C11×#41—41no—
98C11×#41—41no—
99C11×#41—82no—
100C11×#41—82no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11C22⋊C412yes—
104C2×D4×C11—22no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C22⋊C412yes—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C22⋊C412yes—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4C22⋊C412yes—
136C11×C4⋊C4C22⋊C412yes—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C42×C11—24no—
146C42×C11—22no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151#4318—41no—
152#4318—41no—
153#4318—41no—
154#4318—41no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—41no—
157C2×C11⋊C8—42no—
158C2×C11⋊C8—41no—
159C2×C11⋊C8—41no—
160C2×C11⋊C8—41no—
161C2×C11⋊C8—41no—
162#3506D1111yescharacteristic
163#1954—111no—
164#1800—111no—
165#1550—111no—
166#1547—111no—
167#1493—111no—
168#1492—111no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11C2×C22⋊C411yescharacteristic
176Q8×C11—42no—
177Q8×C11—41no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—41no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—41no—
185D4×C11—41no—
186D4×C11—41no—
187D4×C11—41no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—84no—
193D4×C11—84no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—82no—
207C2×C4×C11—84no—
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11#12011yescharacteristic
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#13511yescharacteristic
215C2×C4×C11#13511yescharacteristic
216C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
217C2×C4×C11#13711yescharacteristic
218C11⋊C8—42no—
219C11⋊C8—81no—
220C11⋊C8—81no—
221C11⋊C8—81no—
222#559—22no—
223#556—21no—
224#555—21no—
225#553—22no—
226#550—21no—
227#547—21no—
228#538Dic1114yes—
229#535—21no—
230#533C2×D1111yescharacteristic
231#532C2×D1111yescharacteristic
232#525—22no—
233#520—21no—
234C2×C4×D4C2×D1111yescharacteristic
235#423—111no—
236#423—111no—
237C2×C4⋊C8—111no—
238C2×#100—221no—
239C2×C22⋊C8—222no—
240C2×C4×C8—111no—
241#343—221no—
242#333—221no—
243#332—221no—
244#332—221no—
245#331—221no—
246Q8⋊C8—222no—
247D4⋊C8—222no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—44no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—82no—
258C22×C11#37911yescharacteristic
259C22×C11#41611yescharacteristic
260C22×C11#41711yescharacteristic
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11#44911yescharacteristic
269C4×C11#44911yescharacteristic
270C4×C11#45211yescharacteristic
271C4×C11#45211yescharacteristic
272C4×C11#45311yescharacteristic
273C4×C11#45511yescharacteristic
274C2×#41—22no—
275C2×#41—21no—
276C22×D4C22⋊D1111yescharacteristic
277C23×C4C22⋊D1112yes—
278C2×M16—221no—
279C2×M16—221no—
280C22×C8—221no—
281C22×C8—221no—
282C4⋊Q8C22⋊D1111yescharacteristic
283C4⋊Q8C22⋊D1111yescharacteristic
284C4⋊Q8C22⋊D1111yescharacteristic
285#127—22no—
286#127C22⋊D1111yescharacteristic
287#126—24no—
288#125—21no—
289#124—22no—
290#124—24no—
291#124—21no—
292#123—24no—
293#123—24no—
294C22⋊Q8—22no—
295C22⋊Q8—21no—
296C22⋊Q8C2×Dic1112yes—
297#121—22no—
298#121—22no—
299#121—22no—
300#121—24no—
301#121—21no—
302#121C2×Dic1112yes—
303#120—24no—
304C4×Q8—22no—
305C4×Q8—21no—
306C4×Q8C22⋊D1112yes—
307C4×D4—22no—
308C4×D4—24no—
309C4×D4—24no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4C22⋊D1112yes—
316#117—22no—
317#117—22no—
318#117—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C22⋊C4C2×Dic1112yes—
322C2×C42C22×D1111yescharacteristic
323C4⋊C8—221no—
324C4⋊C8—221no—
325C4⋊C8—221no—
326C4⋊C8—221no—
327C4⋊C8—221no—
328C4⋊C8—221no—
329#100—442no—
330C22⋊C8—444no—
331C4×C8—221no—
332C4×C8—221no—
333C2×C11—21no—
334C2×C11—21no—
335C2×C11—82no—
336C2×C11—82no—
337C2×C11#178811yescharacteristic
338C2×C11#179111yescharacteristic
339C2×C11#179211yescharacteristic
340C24C22⋊Dic1112yes—
341#41—41no—
342#41—41no—
343#41—41no—
344#41—41no—
345#41—82no—
346#41—82no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8C22⋊Dic1112yes—
350C2×D4—22no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4C22⋊Dic1112yes—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4C22⋊Dic1112yes—
369C22×C4C22×Dic1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372M16—441no—
373M16—441no—
374M16—441no—
375M16—441no—
376C2×C8—222no—
377C2×C8—441no—
378C2×C8—441no—
379C2×C8—442no—
380C2×C8—441no—
381C2×C8—441no—
382C2×C8—441no—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4C22⋊Dic1112yes—
393C4⋊C4C22⋊Dic1112yes—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C42—24no—
403C42—22no—
404C42C2×C22⋊D1111yescharacteristic
405C42C2×C22⋊D1111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C2×C22⋊D1111yescharacteristic
408C11#835811yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—42no—
414C23—42no—
415C23C2×C22⋊Dic1111yescharacteristic
416Q8—42no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—41no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—41no—
431D4—41no—
432D4—84no—
433D4—84no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4—84no—
448C2×C4#6700211yescharacteristic
449C2×C4#6700311yescharacteristic
450C2×C4#6700311yescharacteristic
451C2×C4#6700411yescharacteristic
452C2×C4C2×C22⋊Dic1111yescharacteristic
453C2×C4C2×C22⋊Dic1111yescharacteristic
454C2×C4#6700611yescharacteristic
455C2×C4#6700611yescharacteristic
456C2×C4#6700611yescharacteristic
457C2×C4#6700611yescharacteristic
458C8—442no—
459C8—881no—
460C8—881no—
461C8—881no—
462C22—21no—
463C22—21no—
464C22—44no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—82no—
472C22#1062284511yescharacteristic
473C22#1062284611yescharacteristic
474C22#1062286011yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4#1062285111yescharacteristic
483C4#1062285111yescharacteristic
484C4#1062285211yescharacteristic
485C4#1062285211yescharacteristic
486C4#1062285411yescharacteristic
487C4#1062285511yescharacteristic
488C2—21no—
489C2—21no—
490C2—82no—
491C2—82no—
492C2#1306855611yescharacteristic
493C2#1306856711yescharacteristic
494C2#1306857011yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3506C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenter#3506D11
hypocenterC11#8358
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13069411C2semidirect
2. #13068608C2semidirect
3. #13067306C2semidirect
4. #13067293C2semidirect
5. #13067071C2semidirect
6. #13067067C2semidirect
408. C11#8358semidirect

Maximal subgroups

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

subgroupindex
#130694112
#130686082
#130673062
#130672932
#130670712
#130670672
C11×#35062
#835811