Finite Group Databasebeta

← #14647136

Subgroups — #14647136

Order 2816.

540 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071020C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic
3C4×(C2×D11)⋊C8C211yesmaximal, characteristic
4#13066457C211yesmaximal, characteristic, complemented
5#13066456C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×#66925—21no—
9C2×C42×D11C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15#10622600C411yescharacteristic
16#10622600C411yescharacteristic
17#10622589C411yescharacteristic
18#10622589C411yescharacteristic
19C4×C4⋊Dic11C2211yescharacteristic
20C4×Dic11⋊C4—21no—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622280—21no—
24#10622263—21no—
25#10622188—21no—
26#10622188—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66925—42no—
51#66925—42no—
52C42×D11—21no—
53C42×D11—21no—
54C42×D11—21no—
55C42×D11—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60C11×#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64(C2×D11)⋊C8—24no—
65(C2×D11)⋊C8—42no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#8710—111nomaximal, Sylow
71C23×D11C22⋊C411yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C2×C4×D11—22no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—41no—
96C2×C4×D11SD1612yes—
97C2×C4×D11Q1612yes—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11#4111yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138#2285—111no—
139#1797—111no—
140C4×C22⋊C8—111no—
141#1279—111no—
142#1279—111no—
143#1279—111no—
144#1279D1111yescharacteristic, complemented
145C23×C11C2×C22⋊C411yescharacteristic
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11#10312yes—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11#11711yescharacteristic
162C2×C4×C11#11711yescharacteristic
163C2×C4×C11#12311yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C2×C4×C11#13111yescharacteristic
168C2×C4×C11#13111yescharacteristic
169C2×C4×C11#13111yescharacteristic
170C2×C4×C11#13111yescharacteristic
171C2×C4×C11C2×SD1611yescharacteristic
172C2×C4×C11C2×Q1611yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11#10312yes—
189C2×Dic11#10412yes—
190C4×D11—22no—
191C4×D11—22no—
192C4×D11—22no—
193C4×D11—22no—
194C4×D11—42no—
195C4×D11—42no—
196C4×D11—41no—
197C4×D11—41no—
198C4×D11—41no—
199C4×D11—41no—
200C8×C11—42no—
201C8×C11—81no—
202C11⋊C8—42no—
203C11⋊C8—81no—
204C2×#117—221no—
205C22×C42—111no—
206C2×C4⋊C8—111no—
207C2×C4⋊C8C2×D1111yescharacteristic
208C2×C22⋊C8—221no—
209C2×C22⋊C8—221no—
210C2×C4×C8—111no—
211C2×C4×C8C2×D1111yescharacteristic
212#384—111no—
213#384—111no—
214#382—221no—
215#380—111no—
216#380—111no—
217#380—221no—
218C4×C4⋊C4—111no—
219C4×C4⋊C4—221no—
220C4×C4⋊C4C2×D1111yescharacteristic
221#336—221no—
222#336—221no—
223C22×C11#38111yescharacteristic
224C22×C11#40811yescharacteristic
225C22×C11#40811yescharacteristic
226C22×C11C2×#10311yescharacteristic
227C22×C11#41811yescharacteristic
228C22×C11C2×#10411yescharacteristic
229C22×C11#42111yescharacteristic
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11#43311yescharacteristic
242C4×C11#43311yescharacteristic
243C4×C11#43311yescharacteristic
244C4×C11#43311yescharacteristic
245C4×C11#48111yescharacteristic
246C4×C11#48111yescharacteristic
247C4×C11#48411yescharacteristic
248C4×C11#48411yescharacteristic
249Dic11—22no—
250Dic11—22no—
251Dic11—41no—
252Dic11—81no—
253Dic11—81no—
254C23×C4—111no—
255C23×C4—111no—
256C23×C4—111no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—221no—
260C22×C8—221no—
261#117—442no—
262#117—442no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4C4×D1111yescharacteristic
270C2×C4⋊C4C4×D1111yescharacteristic
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C42—21no—
274C2×C42—111no—
275C2×C42—111no—
276C2×C42—111no—
277C2×C42—221no—
278C2×C42—221no—
279C2×C42—221no—
280C2×C42—221no—
281C2×C42—221no—
282C2×C42C22×D1111yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—221no—
286C4⋊C8—221no—
287C22⋊C8—224no—
288C22⋊C8—442no—
289C4×C8—21no—
290C4×C8—21no—
291C4×C8—221no—
292C4×C8—221no—
293#95—21no—
294#95—221no—
295#95—221no—
296#95—221no—
297C2×C11#148111yescharacteristic
298C2×C11#148411yescharacteristic
299C2×C11#149311yescharacteristic
300C2×C11#149611yescharacteristic
301C2×C11#181811yescharacteristic
302C2×C11#182411yescharacteristic
303C2×C11#182611yescharacteristic
304D11—42no—
305C24—111no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—112no—
311C22×C4—112no—
312C22×C4—111no—
313C22×C4—222no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—441no—
329C22×C4C2×C4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—222no—
339C2×C8—441no—
340C2×C8—441no—
341C2×C8—441no—
342C2×C8—441no—
343C2×C8—441no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—442no—
353C4⋊C4—442no—
354C4⋊C4—442no—
355C4⋊C4—442no—
356C22⋊C4—442no—
357C22⋊C4—442no—
358C42—41no—
359C42—41no—
360C42—221no—
361C42—221no—
362C42—221no—
363C42—221no—
364C42—221no—
365C42—221no—
366C42—441no—
367C42—441no—
368C42#433911yescharacteristic
369C42#433911yescharacteristic
370C42#434111yescharacteristic
371C42#434311yescharacteristic
372C11#871011yescharacteristic, complemented, Sylow
373C23—112no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23—221no—
379C23—221no—
380C23C22⋊C4×D1111yescharacteristic
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—112no—
390C2×C4—112no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4#6692511yescharacteristic
415C2×C4#6693611yescharacteristic
416C2×C4#6693611yescharacteristic
417C2×C4#6694511yescharacteristic
418C2×C4#6694711yescharacteristic
419C2×C4#6694711yescharacteristic
420C2×C4#6695411yescharacteristic
421C2×C4#6695411yescharacteristic
422C2×C4#6696011yescharacteristic
423C2×C4#6696011yescharacteristic
424C2×C4#6696411yescharacteristic
425C2×C4SD16×D1111yescharacteristic
426C2×C4#6696711yescharacteristic
427C2×C4Q16×D1111yescharacteristic
428C8—42no—
429C8—81no—
430C8—442no—
431C8—881no—
432C22—222no—
433C22—222no—
434C22—222no—
435C22—441no—
436C22—441no—
437C22—441no—
438C22—441no—
439C22#1062227711yescharacteristic
440C22#1062234011yescharacteristic
441C22#1062234011yescharacteristic
442C22#1062238311yescharacteristic
443C22D11×#10311yescharacteristic
444C22D11×#10411yescharacteristic
445C22#1062243411yescharacteristic
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—222no—
451C4—222no—
452C4—441no—
453C4—881no—
454C4—881no—
455C4#1062230311yescharacteristic
456C4#1062232211yescharacteristic
457C4#1062239011yescharacteristic
458C4#1062242211yescharacteristic
459C4#1062245311yescharacteristic
460C4#1062245311yescharacteristic
461C4#1062247611yescharacteristic
462C4#1062249711yescharacteristic
463C2—442no—
464C2#1306701711yescharacteristic
465C2#1306703111yescharacteristic
466C2#1306706911yescharacteristic
467C2#1306708311yescharacteristic
468C2#1306868611yescharacteristic
469C2#1306870511yescharacteristic
470C2#1306871411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1279D11
hypocenterC11#8710
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #13066457C2semidirect
5. #13066456C2semidirect
6. #13066455C2semidirect
7. C11×#1279C2semidirect
144. #1279D11semidirect
372. C11#8710semidirect

Maximal subgroups

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

subgroupindex
#130710202
#130685932
C4×(C2×D11)⋊C82
#130664572
#130664562
#130664552
C11×#12792
#871011