Finite Group Databasebeta

← #14645262

Subgroups — #14645262

Order 2816.

1082 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic, complemented
3#13068593C211yesmaximal, characteristic, complemented
4C2×#10622120C211yesmaximal, characteristic, complemented
5C2×#10622124C211yesmaximal, characteristic, complemented
6C2×#10622182C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C22×#4341—21no—
9C2×C11×#127C2211yescharacteristic
10C2×#66991—21no—
11C2×#66991C412yes—
12C2×#66989—21no—
13C2×D4×Dic11—21no—
14C2×D4×Dic11C412yes—
15#10623247—22no—
16#10623247—22no—
17#10623247—22no—
18#10623247—22no—
19C2×C42×D11C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8—21no—
24C2×(C2×D11)⋊C8—21no—
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C11×#331—22no—
28#10622188—21no—
29#10622188—21no—
30#10622182—22no—
31#10622124—22no—
32#10622120—22no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11C2×C412yes—
36C22×C22⋊D11—22no—
37C23×Dic11—22no—
38C2×#4341—24no—
39C2×#4341—24no—
40C2×#4341—42no—
41C2×#4341—42no—
42C2×#4341—42no—
43C2×#4341—42no—
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×Dic22—21no—
48C22×C8×C11—21no—
49C22×C8×C11—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127D412yes—
53C11×#127D412yes—
54C2×C42×C11C2311yescharacteristic
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57#66991—24no—
58#66991—24no—
59#66991—24no—
60#66991—24no—
61#66989—24no—
62#66989—24no—
63D4×Dic11—24no—
64D4×Dic11—24no—
65D4×Dic11—24no—
66D4×Dic11—24no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2×C412yes—
69C2×C4×Dic11C2×C411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C22×C11⋊C8—21no—
73C22×C11⋊C8—21no—
74C42×D11—21no—
75C42×D11—21no—
76C42×D11—21no—
77C42×D11—21no—
78#66922—21no—
79#66922—21no—
80#66922D412yes—
81#66922D412yes—
82C11×C4⋊C8—21no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8—21no—
86(C2×D11)⋊C8—42no—
87(C2×D11)⋊C8—42no—
88C4⋊(C11⋊C8)—21no—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)—21no—
92#8341—111nomaximal, Sylow
93C24×C11—22no—
94C23×D11C22⋊C411yescharacteristic
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11C22⋊C414yes—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C2×C22⋊D11—28no—
115C2×C22⋊D11—44no—
116C2×C22⋊D11—44no—
117C22×Dic11—28no—
118C22×Dic11—22no—
119C22×Dic11—44no—
120C22×Dic11—44no—
121C22×Dic11C22⋊C411yescharacteristic
122C22×Dic11C22⋊C411yescharacteristic
123C22×Dic11C22⋊C411yescharacteristic
124#4341—48no—
125#4341—48no—
126#4341—48no—
127#4341—48no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×C4×D11D812yes—
143C2×C4×D11SD1612yes—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—41no—
147C2×Dic22—41no—
148C2×Dic22—41no—
149C2×Dic22—41no—
150C2×C8×C11—41no—
151C2×C8×C11—41no—
152C2×C8×C11—41no—
153C2×C8×C11—41no—
154C2×C8×C11—41no—
155C2×C8×C11—41no—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C22⋊Dic11—28no—
161C22⋊Dic11—28no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11C22⋊C414yes—
166C4×Dic11—21no—
167C4×Dic11—21no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170C4×Dic11—21no—
171C4×Dic11—21no—
172C2×C11⋊C8—41no—
173C2×C11⋊C8—41no—
174C2×C11⋊C8—41no—
175C2×C11⋊C8—41no—
176C2×C11⋊C8—41no—
177C2×C11⋊C8—41no—
178C2×#532—111no—
179#1797—111no—
180#1797—111no—
181C2×#332—111no—
182C2×#332—111no—
183C2×#331—111no—
184C2×#331D1111yescharacteristic, complemented
185C23×C11—24no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11C2×C22⋊C411yescharacteristic
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—21no—
199C22×D11#10212yes—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—42no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C2×SD1611yescharacteristic
220C2×C4×C11#13511yescharacteristic
221C2×C4×C11#13511yescharacteristic
222C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
223C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
224C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
225C2×C4×C11#13711yescharacteristic
226C22⋊D11—416no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—24no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—416no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11#10212yes—
240C4×D11—22no—
241C4×D11—22no—
242C4×D11—22no—
243C4×D11—22no—
244C4×D11—42no—
245C4×D11—42no—
246C4×D11—41no—
247C4×D11—41no—
248C4×D11—41no—
249C4×D11—41no—
250Dic22—42no—
251Dic22—42no—
252Dic22—42no—
253Dic22—42no—
254C8×C11—81no—
255C8×C11—81no—
256C11⋊C8—81no—
257C11⋊C8—81no—
258C22×#41—221no—
259#532—222no—
260#532—222no—
261#532—222no—
262#532—222no—
263C2×C4⋊Q8—111no—
264C2×#127C2×D1111yescharacteristic
265C2×#124—221no—
266C2×#121—112no—
267C2×#121—221no—
268C2×C4×D4—112no—
269C2×C4×D4—221no—
270C22×C42—111no—
271C2×C4⋊C8—111no—
272C2×C4⋊C8—111no—
273C2×C4⋊C8C2×D1111yescharacteristic
274C2×C4⋊C8C2×D1111yescharacteristic
275C2×C22⋊C8—221no—
276C2×C22⋊C8—221no—
277#336—221no—
278#336—221no—
279#332—222no—
280#332—222no—
281#331—22no—
282#331—222no—
283C22×C11—44no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11#37911yescharacteristic
291C22×C11#41311yescharacteristic
292C22×C11#41311yescharacteristic
293C22×C11C2×#10211yescharacteristic
294C22×C11#41611yescharacteristic
295C22×C11#41711yescharacteristic
296C22×C11#41811yescharacteristic
297C2×D11—22no—
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—41no—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—41no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11#44711yescharacteristic
307C4×C11#44711yescharacteristic
308C4×C11#44911yescharacteristic
309C4×C11#44911yescharacteristic
310C4×C11#45011yescharacteristic
311C4×C11#45011yescharacteristic
312C4×C11#45211yescharacteristic
313C4×C11#45211yescharacteristic
314Dic11—22no—
315Dic11—41no—
316Dic11—44no—
317Dic11—41no—
318C2×#41—224no—
319C2×#41—224no—
320C2×#41—442no—
321C2×#41—442no—
322C2×#41—442no—
323C2×#41—442no—
324C22×Q8—221no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—222no—
328C22×D4C4×D1112yes—
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—111no—
332C23×C4—222no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—221no—
336C22×C8—221no—
337C4⋊Q8—112no—
338C4⋊Q8—112no—
339C4⋊Q8—221no—
340C4⋊Q8—221no—
341#127—21no—
342#127—21no—
343#127D4412yes—
344#127C22⋊D1112yes—
345#124—224no—
346#124—224no—
347#121—224no—
348#121—224no—
349#121—224no—
350#121—224no—
351C4×D4—224no—
352C4×D4—224no—
353C4×D4—224no—
354C4×D4—224no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—221no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—111no—
362C2×C42—221no—
363C2×C42—221no—
364C2×C42—221no—
365C2×C42—221no—
366C2×C42C22×D1111yescharacteristic
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—21no—
371C4⋊C8—221no—
372C4⋊C8—221no—
373C4⋊C8—221no—
374C4⋊C8—221no—
375C22⋊C8—442no—
376C22⋊C8—442no—
377C2×C11—84no—
378C2×C11#154011yescharacteristic
379C2×C11#154711yescharacteristic
380C2×C11#155311yescharacteristic
381C2×C11#155711yescharacteristic
382C2×C11#178511yescharacteristic
383C2×C11#178611yescharacteristic
384C2×C11#178811yescharacteristic
385D11—42no—
386C24—22no—
387C24—111no—
388#41—448no—
389#41—448no—
390#41—448no—
391#41—448no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—441no—
395C2×Q8—441no—
396C2×Q8—441no—
397C2×Q8—441no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—228no—
414C2×D4—444no—
415C2×D4—444no—
416C2×D4(C2×D11)⋊C414yes—
417C22×C4—111no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—228no—
427C22×C4—222no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—441no—
437C22×C4—441no—
438C22×C4—444no—
439C22×C4—444no—
440C22×C4C2×C4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1111yescharacteristic
443C2×C8—41no—
444C2×C8—41no—
445C2×C8—41no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—41no—
449C2×C8—441no—
450C2×C8—441no—
451C2×C8—441no—
452C2×C8—441no—
453C2×C8—441no—
454C2×C8—441no—
455C4⋊C4—114no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C42—221no—
462C42—221no—
463C42—221no—
464C42—221no—
465C42—221no—
466C42—221no—
467C42C2×D4411yescharacteristic
468C42D4×D1111yescharacteristic
469C42D4×D1111yescharacteristic
470C42C2×C22⋊D1111yescharacteristic
471C11#834111yescharacteristic, complemented, Sylow
472C23—24no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—112no—
480C23—221no—
481C23—221no—
482C23—221no—
483C23—221no—
484C23—221no—
485C23—221no—
486C23C22⋊C4×D1111yescharacteristic
487Q8—442no—
488Q8—442no—
489Q8—442no—
490Q8—442no—
491D4—44no—
492D4—44no—
493D4—42no—
494D4—42no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—4416no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—112no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—224no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—4416no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4C22⋊C4×D1111yescharacteristic
528C2×C4#6693511yescharacteristic
529C2×C4#6693511yescharacteristic
530C2×C4D8×D1111yescharacteristic
531C2×C4#6696411yescharacteristic
532C2×C4#6696411yescharacteristic
533C2×C4#6696511yescharacteristic
534C2×C4SD16×D1111yescharacteristic
535C2×C4#6696711yescharacteristic
536C2×C4#6696811yescharacteristic
537C2×C4#6696911yescharacteristic
538C2×C4C2×(C2×D11)⋊C411yescharacteristic
539C2×C4#6699011yescharacteristic
540C2×C4#6699011yescharacteristic
541C8—81no—
542C8—81no—
543C8—881no—
544C8—881no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—222no—
553C22—222no—
554C22—222no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22—441no—
559C22#1062235811yescharacteristic
560C22#1062235811yescharacteristic
561C22D11×#10211yescharacteristic
562C22#1062238311yescharacteristic
563C22#1062238411yescharacteristic
564C22#1062238511yescharacteristic
565C22#1062256811yescharacteristic
566C4—21no—
567C4—21no—
568C4—222no—
569C4—444no—
570C4—441no—
571C4—441no—
572C4#1062238611yescharacteristic
573C4#1062238911yescharacteristic
574C4#1062239411yescharacteristic
575C4#1062239611yescharacteristic
576C4#1062276911yescharacteristic
577C4#1062277111yescharacteristic
578C4#1062278211yescharacteristic
579C4#1062278611yescharacteristic
580C2—84no—
581C2—442no—
582C2#1306726211yescharacteristic
583C2#1306729011yescharacteristic
584C2#1306731811yescharacteristic
585C2#1306733511yescharacteristic
586C2#1306854111yescharacteristic
587C2#1306854511yescharacteristic
588C2#1306855311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623247C2
cosocleC2×C42×C11C23
hypercenterC2×#331D11
hypocenterC11#8341
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #13068593C2semidirect
3. #13068593C2semidirect
4. C2×#10622120C2semidirect
5. C2×#10622124C2semidirect
6. C2×#10622182C2semidirect
7. C2×C11×#331C2semidirect
184. C2×#331D11semidirect
471. C11#8341semidirect

Maximal subgroups

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

subgroupindex
C2×#106232472
#130685932
C2×#106221202
C2×#106221242
C2×#106221822
C2×C11×#3312
#834111