Finite Group Databasebeta

← #14648323

Subgroups — #14648323

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622448C211yesmaximal, characteristic, complemented
2C4×#66948C211yesmaximal, characteristic
3C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×#10622097C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6#13066457C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×#66948C411yescharacteristic
9C2×C4×D44—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C42×D11C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15C2×(C2×D11)⋊C8—21no—
16C2×(C2×D11)⋊C8—21no—
17C2×#66879—21no—
18#10622601C411yescharacteristic
19#10622600C411yescharacteristic
20#10622598C411yescharacteristic
21C4×(C2×D11)⋊C4—21no—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622448—22no—
25#10622448—22no—
26#10622283—21no—
27#10622278—21no—
28#10622188—21no—
29#10622121—22no—
30#10622097—22no—
31C22×D44—21no—
32C22×D44C2×C411yescharacteristic
33C22×C4×D11—21no—
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
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×Dic11C2×C411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C22×C11⋊C8—21no—
54C22×C11⋊C8—21no—
55#66948—22no—
56#66948—22no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—42no—
62C4×D44—42no—
63C42×D11—21no—
64C42×D11—21no—
65C42×D11—21no—
66C42×D11—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yescomplemented
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71C11×#95—21no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74(C2×D11)⋊C8—24no—
75(C2×D11)⋊C8—24no—
76#66879—24no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)D412yescomplemented
79C4×C11⋊C8—21no—
80C4×C11⋊C8—21no—
81#8943—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—24no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—42no—
100C2×D44—42no—
101C2×D44M1612yes—
102C2×C4×D11—22no—
103C2×C4×D11—21no—
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—21no—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—41no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4M1612yes—
134C42×C11—41no—
135C42×C11—41no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11#4111yescharacteristic
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—42no—
142(C2×D11)⋊C4—42no—
143(C2×D11)⋊C4—42no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—42no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152C4×Dic11—21no—
153C4×Dic11—21no—
154C4×Dic11—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—41no—
158C2×C11⋊C8—41no—
159C2×C11⋊C8—41no—
160C2×C11⋊C8—41no—
161C2×#432—111no—
162C4×#121—111no—
163C4×C22⋊C8—111no—
164C2×D4⋊C8—111no—
165C2×D4⋊C8—111no—
166#1279—111no—
167#1279D1111yescharacteristic, complemented
168C23×C11C2×C22⋊C411yescharacteristic
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11#10412yes—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11C4×D411yescharacteristic
192C2×C4×C11C4×D411yescharacteristic
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12311yescharacteristic
197C2×C4×C11C2×M1611yescharacteristic
198C2×C4×C11C2×M1611yescharacteristic
199C2×C4×C11#13111yescharacteristic
200C2×C4×C11#13111yescharacteristic
201C2×C4×C11#13511yescharacteristic
202C2×C4×C11#13511yescharacteristic
203C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217D44—22no—
218D44—22no—
219D44—48no—
220D44—41no—
221D44—41no—
222C4×D11—42no—
223C4×D11—42no—
224C4×D11—41no—
225C4×D11—41no—
226C4×D11—41no—
227C4×D11—41no—
228C4×D11—41no—
229C4×D11—41no—
230C4×D11—41no—
231C4×D11—41no—
232C4×D11—81no—
233C4×D11—81no—
234C4×D11—81no—
235C4×D11—81no—
236C8×C11—42no—
237C8×C11—42no—
238C11⋊C8—42no—
239C11⋊C8—42no—
240C2×#121—111no—
241C2×C4×D4—111no—
242C2×C4×D4—221no—
243C22×C42—111no—
244#432—222no—
245#432—222no—
246C2×C4⋊C8—111no—
247C2×C4⋊C8C2×D1111yescharacteristic
248C2×C22⋊C8—221no—
249C2×C22⋊C8—221no—
250C2×#97—221no—
251C2×C4×C8—111no—
252C2×C4×C8C2×D1111yescharacteristic
253#390—111no—
254#389—111no—
255#388—221no—
256#386—221no—
257#380—111no—
258C4×C4⋊C4C2×D1111yescharacteristic
259C4×C22⋊C4—221no—
260#336—221no—
261D4⋊C8—222no—
262D4⋊C8—222no—
263C22×C11#38611yescharacteristic
264C22×C11#40711yescharacteristic
265C22×C11#40811yescharacteristic
266C22×C11#41611yescharacteristic
267C22×C11#41811yescharacteristic
268C22×C11C2×#10411yescharacteristic
269C22×C11#42111yescharacteristic
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—41no—
274C2×D11—41no—
275C2×D11—41no—
276C2×D11—41no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—81no—
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—42no—
287C4×C11—81no—
288C4×C11#43511yescharacteristic
289C4×C11#43511yescharacteristic
290C4×C11#43611yescharacteristic
291C4×C11#43611yescharacteristic
292C4×C11#44911yescharacteristic
293C4×C11#44911yescharacteristic
294C4×C11#48211yescharacteristic
295C4×C11#48211yescharacteristic
296Dic11—41no—
297Dic11—41no—
298Dic11—41no—
299Dic11—81no—
300C22×D4—111no—
301C22×D4—221no—
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—111no—
305C23×C4—221no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—221no—
309C22×C8—221no—
310#121—222no—
311#121—222no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4—221no—
316C4×D4—442no—
317C4×D4—442no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4C4×D1111yescharacteristic
321C2×C4⋊C4C4×D1111yescharacteristic
322C2×C22⋊C4—221no—
323C2×C22⋊C4—221no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C42—21no—
328C2×C42—111no—
329C2×C42—111no—
330C2×C42—111no—
331C2×C42—221no—
332C2×C42—221no—
333C2×C42—221no—
334C2×C42—221no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—112no—
338C4⋊C8—221no—
339C4⋊C8D4412yescomplemented
340C22⋊C8—224no—
341C22⋊C8—224no—
342#97—224no—
343C4×C8—21no—
344C4×C8—21no—
345C4×C8—221no—
346C4×C8—221no—
347#95—21no—
348#95—221no—
349#95—221no—
350C2×C11#148811yescharacteristic
351C2×C11#149011yescharacteristic
352C2×C11#149411yescharacteristic
353C2×C11#149611yescharacteristic
354C2×C11#187011yescharacteristic
355C2×C11#187111yescharacteristic
356C2×C11#187511yescharacteristic
357D11—42no—
358D11—82no—
359C24—111no—
360C24—221no—
361C2×D4—112no—
362C2×D4—224no—
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—442no—
369C2×D4—442no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—222no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4C2×C4×D1111yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—222no—
408C2×C8—222no—
409C2×C8—441no—
410C2×C8—441no—
411C2×C8—441no—
412C2×C8—441no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C4⋊C4—442no—
419C4⋊C4#431312yes—
420C22⋊C4—224no—
421C22⋊C4—442no—
422C22⋊C4—442no—
423C22⋊C4—442no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C42—41no—
427C42—41no—
428C42—221no—
429C42—221no—
430C42—221no—
431C42—221no—
432C42—221no—
433C42—221no—
434C42C2×D4411yescharacteristic
435C42#433911yescharacteristic
436C42D4×D1111yescharacteristic
437C42#434311yescharacteristic
438C11#894311yescharacteristic, complemented, Sylow
439C23—112no—
440C23—221no—
441C23—221no—
442C23—221no—
443C23—221no—
444C23—221no—
445C23—221no—
446C23—222no—
447C23—441no—
448C23—441no—
449C23—441no—
450C23—441no—
451C23—441no—
452C23—441no—
453C23C22⋊C4×D1111yescharacteristic
454D4—222no—
455D4—222no—
456D4—448no—
457D4—441no—
458D4—441no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—881no—
490C2×C4—881no—
491C2×C4—881no—
492C2×C4—881no—
493C2×C4C4×D4411yescharacteristic
494C2×C4#6693511yescharacteristic
495C2×C4#6693711yescharacteristic
496C2×C4#6694611yescharacteristic
497C2×C4#6694711yescharacteristic
498C2×C4#6694811yescharacteristic
499C2×C4C2×#431311yescharacteristic
500C2×C4#6695411yescharacteristic
501C2×C4M16×D1111yescharacteristic
502C2×C4#6696011yescharacteristic
503C2×C4#6696411yescharacteristic
504C2×C4#6696711yescharacteristic
505C2×C4#6696911yescharacteristic
506C2×C4#6697211yescharacteristic
507C8—42no—
508C8—42no—
509C8—442no—
510C8—442no—
511C22—222no—
512C22—222no—
513C22—222no—
514C22—441no—
515C22—441no—
516C22—441no—
517C22—441no—
518C22—442no—
519C22—442no—
520C22—442no—
521C22—881no—
522C22—881no—
523C22—881no—
524C22—881no—
525C22#1062227811yescharacteristic
526C22#1062233911yescharacteristic
527C22#1062234011yescharacteristic
528C22#1062238311yescharacteristic
529C22#1062241711yescharacteristic
530C22D11×#10411yescharacteristic
531C22#1062243411yescharacteristic
532C4—21no—
533C4—21no—
534C4—42no—
535C4—81no—
536C4—441no—
537C4—441no—
538C4—441no—
539C4—881no—
540C4#1062230111yescharacteristic
541C4#1062231911yescharacteristic
542C4#1062239411yescharacteristic
543C4#1062242411yescharacteristic
544C4#1062244911yescharacteristic
545C4#1062245111yescharacteristic
546C4#1062247911yescharacteristic
547C4#1062249811yescharacteristic
548C2—442no—
549C2—882no—
550C2#1306704911yescharacteristic
551C2#1306705711yescharacteristic
552C2#1306707511yescharacteristic
553C2#1306708311yescharacteristic
554C2#1306891211yescharacteristic
555C2#1306891711yescharacteristic
556C2#1306893711yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66948C4
cosocleC2×C42×C11C23
hypercenter#1279D11
hypocenterC11#8943
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
1. C2×#10622448C2semidirect
3. C4×(C2×D11)⋊C8C2semidirect
4. C2×#10622097C2semidirect
5. C2×#10622121C2semidirect
6. #13066457C2semidirect
7. C11×#1279C2semidirect
68. C11×C4⋊C8D4semidirect
78. C4⋊(C11⋊C8)D4semidirect
167. #1279D11semidirect
339. C4⋊C8D44semidirect
438. C11#8943semidirect

Maximal subgroups

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

subgroupindex
C2×#106224482
C4×#669482
C4×(C2×D11)⋊C82
C2×#106220972
C2×#106221212
#130664572
C11×#12792
#894311