Finite Group Databasebeta

← #14649367

Subgroups — #14649367

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#97C211yesmaximal, characteristic, complemented
2#13076918C211yesmaximal, characteristic
3#13068379C211yesmaximal, characteristic, complemented
4C2×#10622102C211yesmaximal, characteristic, complemented
5C2×#10622102C211yesmaximal, characteristic, complemented
6#13066497C211yesmaximal, characteristic, complemented
7C11×#1295C211yesmaximal, characteristic, complemented
8C22×C8×D11—21no—
9C2×#66950C411yescharacteristic
10C2×#66948C411yescharacteristic
11C2×#66928C2211yescharacteristic
12C2×C42×D11C2211yescharacteristic
13C2×C11×#97C2211yescharacteristic
14C2×C11×#97C2211yescharacteristic
15C11×#382C2211yescharacteristic
16C2×(C2×D11)⋊C8—21no—
17C2×#66879—21no—
18#10622601C411yescharacteristic
19#10622587C411yescharacteristic
20C2×#66867C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22D11×#97—22no—
23D11×#97—22no—
24#10622283—21no—
25#10622283—21no—
26#10622278—21no—
27#10622278—21no—
28#10622188—21no—
29#10622102—22no—
30#10622102—22no—
31C22×D44—21no—
32C22×D44C2×C411yescharacteristic
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×Dic22C2×C411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11—21no—
49C2×C4×Dic11C2×C411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C2×C8×D11—24no—
55C2×C8×D11—24no—
56C2×C8×D11—24no—
57#66950—42no—
58#66948—42no—
59#66928—21no—
60#66928—21no—
61#66928—21no—
62#66928—21no—
63C42×D11—21no—
64C42×D11—21no—
65C42×D11—21no—
66C42×D11—21no—
67C11×#97—21no—
68C11×#97—21no—
69C11×#97—21no—
70C11×#97D412yescomplemented
71C11×#95—21no—
72C11×#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75(C2×D11)⋊C8—24no—
76#66879—24no—
77#66867—21no—
78#66867—21no—
79#66867—21no—
80#66867D412yescomplemented
81#9119—111nomaximal, Sylow
82C23×D11—21no—
83C23×D11C22⋊C411yescharacteristic
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—21no—
90C22×Dic11C22⋊C411yescharacteristic
91C22×Dic11C22⋊C411yescharacteristic
92C22×Dic11C22⋊C411yescharacteristic
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—42no—
98C2×D44—42no—
99C2×D44—42no—
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—41no—
115C2×Dic22—41no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11#4111yescharacteristic
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—42no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C8×D11—216no—
150C22×#97—111no—
151#2850—111no—
152#1749—111no—
153C2×#329—111no—
154C2×#329—111no—
155#1295—111no—
156#1295D1111yescharacteristic, complemented
157C23×C11C2×C22⋊C411yescharacteristic
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11#10012yes—
170C22×D11#10412yes—
171C22×D11#10412yes—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
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×C11C4×D411yescharacteristic
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12311yescharacteristic
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11#10412yes—
202D44—81no—
203D44—81no—
204D44—84no—
205C4×D11—24no—
206C4×D11—24no—
207C4×D11—42no—
208C4×D11—42no—
209C4×D11—42no—
210C4×D11—42no—
211Dic22—81no—
212Dic22—81no—
213C8×C11—24no—
214C8×C11—42no—
215C11⋊C8—24no—
216C11⋊C8—42no—
217C23×C8—221no—
218C2×#124—111no—
219C2×C22⋊Q8—111no—
220C2×#121—111no—
221C22×C42—111no—
222C2×C22⋊C8—221no—
223C2×#97—111no—
224C2×#97—111no—
225C2×#97—222no—
226C2×#97—221no—
227C2×#97—222no—
228C2×#97C2×D1111yescharacteristic
229C2×#97C2×D1111yescharacteristic
230#391—111no—
231#390—111no—
232#388—221no—
233#388—221no—
234#386—221no—
235#386—221no—
236#382C2×D1111yescharacteristic
237#336—221no—
238#329—222no—
239#329—222no—
240C22×C11#38611yescharacteristic
241C22×C11C2×#10011yescharacteristic
242C22×C11#41311yescharacteristic
243C22×C11C2×#10411yescharacteristic
244C22×C11C2×#10411yescharacteristic
245C22×C11C2×#10411yescharacteristic
246C22×C11#42111yescharacteristic
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C2×D11—81no—
260C2×D11#32914yescomplemented
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—81no—
268C4×C11—81no—
269Dic11—22no—
270Dic11—41no—
271Dic11—41no—
272Dic11—81no—
273C22×Q8—111no—
274C22×D4—111no—
275C22×D4—221no—
276C23×C4—111no—
277C23×C4—111no—
278C23×C4—111no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—224no—
282C22×C8—224no—
283C22×C8—224no—
284C22×C8—221no—
285C22×C8—221no—
286#124—221no—
287#124—221no—
288#124—221no—
289#124—221no—
290C22⋊Q8—442no—
291#121—442no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4C4×D1111yescharacteristic
294C2×C4⋊C4C4×D1111yescharacteristic
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C42—111no—
302C2×C42—111no—
303C2×C42—111no—
304C2×C42—221no—
305C2×C42—221no—
306C2×C42—221no—
307C2×C42—221no—
308C2×C42C22×D1111yescharacteristic
309C22⋊C8—224no—
310#97—21no—
311#97—21no—
312#97—21no—
313#97—112no—
314#97—224no—
315#97—221no—
316#97—221no—
317#97—221no—
318#97D4412yescomplemented
319#95—21no—
320#95—21no—
321#95—221no—
322#95—221no—
323C2×C11C2×#32911yescharacteristic
324C2×C11#152411yescharacteristic
325C2×C11#153011yescharacteristic
326C2×C11#153211yescharacteristic
327C2×C11#187111yescharacteristic
328C2×C11#189611yescharacteristic
329C2×C11#190011yescharacteristic
330D11—24no—
331D11—161no—
332C24—111no—
333C24—221no—
334C2×Q8—221no—
335C2×Q8—221no—
336C2×Q8—441no—
337C2×Q8—441no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—442no—
343C2×D4—442no—
344C2×D4—442no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—111no—
348C22×C4—111no—
349C22×C4—111no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4C2×C4×D1111yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—2216no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—441no—
378C2×C8—441no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—442no—
382C22⋊C4—442no—
383C22⋊C4—442no—
384C22⋊C4—442no—
385C22⋊C4—442no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C42—221no—
391C42—221no—
392C42—221no—
393C42—221no—
394C42—221no—
395C42—221no—
396C42C2×D4411yescharacteristic
397C42#433911yescharacteristic
398C42D4×D1111yescharacteristic
399C42#434311yescharacteristic
400C11#911911yescharacteristic, complemented, Sylow
401C23—112no—
402C23—112no—
403C23—112no—
404C23—221no—
405C23—221no—
406C23—221no—
407C23—221no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23C22⋊C4×D1111yescharacteristic
416Q8—881no—
417Q8—881no—
418D4—881no—
419D4—881no—
420D4—884no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—112no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4C4×D4411yescharacteristic
452C2×C4#6693511yescharacteristic
453C2×C4#6693711yescharacteristic
454C2×C4#6694611yescharacteristic
455C2×C4#6694711yescharacteristic
456C2×C4#6694811yescharacteristic
457C8—24no—
458C8—42no—
459C8—224no—
460C8—442no—
461C22—114no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22—222no—
466C22—222no—
467C22—222no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22#1062227811yescharacteristic
476C22D11×#10011yescharacteristic
477C22#1062236411yescharacteristic
478C22D11×#10411yescharacteristic
479C22D11×#10411yescharacteristic
480C22D11×#10411yescharacteristic
481C22#1062243411yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—81no—
489C4—81no—
490C4—222no—
491C4—441no—
492C4—441no—
493C4—881no—
494C2—224no—
495C2—1761no—
496C2D11×#32911yescharacteristic
497C2#1306720311yescharacteristic
498C2#1306722511yescharacteristic
499C2#1306723511yescharacteristic
500C2#1306891711yescharacteristic
501C2#1306905811yescharacteristic
502C2#1306907811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66948C4
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#9119
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. C2×D11×#97C2semidirect
3. #13068379C2semidirect
4. C2×#10622102C2semidirect
5. C2×#10622102C2semidirect
6. #13066497C2semidirect
7. C11×#1295C2semidirect
70. C11×#97D4semidirect
80. #66867D4semidirect
156. #1295D11semidirect
260. C2×D11#329semidirect
318. #97D44semidirect
400. C11#9119semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#972
#130769182
#130683792
C2×#106221022
#130664972
C11×#12952
#911911