Finite Group Databasebeta

← #14649392

Subgroups — #14649392

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622318C211yesmaximal, 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
8C2×#66950C411yescharacteristic
9C2×#66948C411yescharacteristic
10C2×#66928C2211yescharacteristic
11C2×C42×D11C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C2×C11×#97C2211yescharacteristic
14C11×#382C2211yescharacteristic
15C2×(C2×D11)⋊C8—21no—
16C2×(C2×D11)⋊C8—21no—
17C2×Dic11⋊C8—21no—
18#10622601C411yescharacteristic
19#10622587C411yescharacteristic
20C2×#66867C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22#10622318—22no—
23#10622318—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—
54#66950—42no—
55#66948—42no—
56#66928—21no—
57#66928—21no—
58#66928—21no—
59#66928—21no—
60C42×D11—21no—
61C42×D11—21no—
62C42×D11—21no—
63C42×D11—21no—
64C11×#97—21no—
65C11×#97—21no—
66C11×#97—21no—
67C11×#97D412yescomplemented
68C11×#95—21no—
69C11×#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72(C2×D11)⋊C8—24no—
73(C2×D11)⋊C8—24no—
74Dic11⋊C8—24no—
75#66867—21no—
76#66867—21no—
77#66867—21no—
78#66867D412yescomplemented
79#9124—111nomaximal, Sylow
80C23×D11—21no—
81C23×D11C22⋊C411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—42no—
96C2×D44—42no—
97C2×D44—42no—
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—21no—
101C2×C4×D11—21no—
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×Dic22—21no—
111C2×Dic22—21no—
112C2×Dic22—41no—
113C2×Dic22—41no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C42×C11#4111yescharacteristic
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134C4⋊Dic11—42no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×#432—111no—
148#2850—111no—
149#1749—111no—
150C2×#329—111no—
151C2×#329—111no—
152#1295—111no—
153#1295D1111yescharacteristic, complemented
154C23×C11C2×C22⋊C411yescharacteristic
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11#10012yes—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
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×C11C4×D411yescharacteristic
182C2×C4×C11C4×D411yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12311yescharacteristic
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11#10412yes—
199D44—81no—
200D44—81no—
201D44—84no—
202C4×D11—42no—
203C4×D11—42no—
204C4×D11—42no—
205C4×D11—42no—
206C4×D11—42no—
207C4×D11—42no—
208Dic22—81no—
209Dic22—81no—
210C8×C11—42no—
211C8×C11—42no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C2×#124—111no—
215C2×C22⋊Q8—111no—
216C2×#121—111no—
217C22×C42—111no—
218#432—222no—
219#432—222no—
220C2×C4⋊C8—221no—
221C2×C22⋊C8—221no—
222C2×C22⋊C8—221no—
223C2×#97—111no—
224C2×#97—111no—
225C2×#97C2×D1111yescharacteristic
226C2×#97C2×D1111yescharacteristic
227#391—111no—
228#390—111no—
229#388—221no—
230#388—221no—
231#386—221no—
232#386—221no—
233#382C2×D1111yescharacteristic
234#336—221no—
235#329—222no—
236#329—222no—
237C22×C11#38611yescharacteristic
238C22×C11C2×#10011yescharacteristic
239C22×C11#41311yescharacteristic
240C22×C11C2×#10411yescharacteristic
241C22×C11#42111yescharacteristic
242C22×C11#42111yescharacteristic
243C22×C11#42111yescharacteristic
244C2×D11—22no—
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—41no—
248C2×D11—41no—
249C2×D11—41no—
250C2×D11—41no—
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—81no—
265C4×C11—81no—
266Dic11—22no—
267Dic11—41no—
268Dic11—41no—
269Dic11—81no—
270C22×Q8—111no—
271C22×D4—111no—
272C22×D4—221no—
273C23×C4—111no—
274C23×C4—111no—
275C23×C4—111no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—221no—
279C22×C8—221no—
280#124—221no—
281#124—221no—
282#124—221no—
283#124—221no—
284C22⋊Q8—442no—
285#121—442no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4C4×D1111yescharacteristic
288C2×C4⋊C4C4×D1111yescharacteristic
289C2×C22⋊C4—221no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—221no—
295C2×C42—111no—
296C2×C42—111no—
297C2×C42—111no—
298C2×C42—221no—
299C2×C42—221no—
300C2×C42—221no—
301C2×C42—221no—
302C2×C42C22×D1111yescharacteristic
303C4⋊C8—224no—
304C22⋊C8—224no—
305C22⋊C8—224no—
306#97—21no—
307#97—21no—
308#97—21no—
309#97—112no—
310#97—221no—
311#97—221no—
312#97—221no—
313#97D4412yescomplemented
314#95—21no—
315#95—21no—
316#95—221no—
317#95—221no—
318C2×C11#152911yescharacteristic
319C2×C11#153011yescharacteristic
320C2×C11#153311yescharacteristic
321C2×C11#153511yescharacteristic
322C2×C11#187111yescharacteristic
323C2×C11#189711yescharacteristic
324C2×C11#190011yescharacteristic
325D11—42no—
326D11—161no—
327C24—111no—
328C24—221no—
329C2×Q8—221no—
330C2×Q8—221no—
331C2×Q8—441no—
332C2×Q8—441no—
333C2×D4—221no—
334C2×D4—221no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4—442no—
338C2×D4—442no—
339C2×D4—442no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4C2×C4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—441no—
370C2×C8—441no—
371C2×C8—441no—
372C2×C8—441no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—442no—
376C22⋊C4—442no—
377C22⋊C4—442no—
378C22⋊C4—442no—
379C22⋊C4—442no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C42—221no—
385C42—221no—
386C42—221no—
387C42—221no—
388C42—221no—
389C42—221no—
390C42C2×D4411yescharacteristic
391C42#433911yescharacteristic
392C42D4×D1111yescharacteristic
393C42#434311yescharacteristic
394C11#912411yescharacteristic, complemented, Sylow
395C23—112no—
396C23—221no—
397C23—221no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23C22⋊C4×D1111yescharacteristic
410Q8—881no—
411Q8—881no—
412D4—881no—
413D4—881no—
414D4—884no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—112no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4C4×D4411yescharacteristic
446C2×C4#6693511yescharacteristic
447C2×C4#6693711yescharacteristic
448C2×C4#6694611yescharacteristic
449C2×C4#6694711yescharacteristic
450C2×C4#6694811yescharacteristic
451C8—42no—
452C8—42no—
453C8—442no—
454C8—442no—
455C22—222no—
456C22—222no—
457C22—222no—
458C22—441no—
459C22—441no—
460C22—441no—
461C22—441no—
462C22—881no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22—881no—
468C22—881no—
469C22#1062227811yescharacteristic
470C22D11×#10011yescharacteristic
471C22#1062236411yescharacteristic
472C22D11×#10411yescharacteristic
473C22#1062243411yescharacteristic
474C22#1062243411yescharacteristic
475C22#1062243411yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—81no—
484C4—222no—
485C4—441no—
486C4—441no—
487C4—881no—
488C2—442no—
489C2—1761no—
490C2#1306722211yescharacteristic
491C2#1306722511yescharacteristic
492C2#1306723811yescharacteristic
493C2#1306724611yescharacteristic
494C2#1306891711yescharacteristic
495C2#1306906311yescharacteristic
496C2#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#9124
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×#10622318C2semidirect
3. #13068379C2semidirect
4. C2×#10622102C2semidirect
5. C2×#10622102C2semidirect
6. #13066497C2semidirect
7. C11×#1295C2semidirect
67. C11×#97D4semidirect
78. #66867D4semidirect
153. #1295D11semidirect
313. #97D44semidirect
394. C11#9124semidirect

Maximal subgroups

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

subgroupindex
C2×#106223182
#130769182
#130683792
C2×#106221022
#130664972
C11×#12952
#912411