Finite Group Databasebeta

← #14671302

Subgroups — #14671302

Order 2816.

910 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072263C211yesmaximal, characteristic
2C2×#10622111C212yesmaximal, complemented
3#13068531C211yesmaximal, characteristic
4#13066740C212yesmaximal, complemented
5C22×C11×#99C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C22×C11×C22⋊C4—21no—
8C2×#66989C411yescharacteristic, complemented
9C2×#66989C2211yescharacteristic
10C2×#66977C411yescharacteristic, complemented
11C2×C11×#99—21no—
12C2×C11×#99—24no—
13C2×C11×#99C2212yes—
14#10622860—21no—
15#10622860—21no—
16#10622860—21no—
17#10622835—21no—
18#10622835—21no—
19#10622834C411yescharacteristic, complemented
20#10622834C2211yescharacteristic
21C2×#66898—21no—
22C2×#66898C2212yes—
23C4×C22⋊Dic11C411yescharacteristic, complemented
24#10622111—24no—
25C25×C11D411yescharacteristic
26C25×C11D411yescharacteristic
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—41no—
30C22×D4×C11—41no—
31C22×D4×C11—42no—
32C22×D4×C11C2×C411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11—41no—
37C23×C4×C11C2×C411yescharacteristic
38C22×Dic22C2×C411yescharacteristic, complemented
39C2×C11×C22⋊C4—24no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—41no—
42C2×C11×C22⋊C4—42no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—41no—
55C2×C22⋊Dic11—41no—
56#66989—22no—
57#66989—22no—
58#66989—42no—
59C2×C4⋊Dic11C2×C411yescharacteristic, complemented
60#66977—41no—
61#66977—41no—
62C2×Dic11⋊C4—21no—
63C2×C4×Dic11C2×C411yescharacteristic, complemented
64C2×C4×Dic11C2×C411yescharacteristic, complemented
65C11×#99—24no—
66C11×#99—22no—
67C11×#99D414yes—
68#66898—22no—
69#66898—22no—
70#66898—42no—
71C11⋊#95—21no—
72#13090—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11—22no—
75C24×C11—21no—
76C24×C11—21no—
77C24×C11—21no—
78C24×C11—21no—
79C24×C11—21no—
80C24×C11—22no—
81C24×C11—41no—
82C24×C11—42no—
83C24×C11—42no—
84C24×C11—81no—
85C24×C11—81no—
86C24×C11C22⋊C411yescharacteristic
87C24×C11C22⋊C411yescharacteristic
88C24×C11C22⋊C411yescharacteristic
89C24×C11C2×D411yescharacteristic
90C24×C11C2×D411yescharacteristic
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—44no—
107C2×D4×C11C2×D412yes—
108C2×D4×C11#4112yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—41no—
113C22×C4×C11—44no—
114C22×C4×C11—42no—
115C22×C4×C11—82no—
116C22×C4×C11—82no—
117C22×C4×C11C22⋊C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—42no—
124C2×Dic22—22no—
125C2×Dic22—41no—
126C2×Dic22—41no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—44no—
129C11×C22⋊C4—42no—
130C22⋊Dic11—42no—
131C22⋊Dic11—42no—
132C22⋊Dic11—42no—
133C22⋊Dic11—41no—
134C22⋊Dic11—41no—
135C22⋊Dic11—42no—
136C22⋊Dic11—41no—
137C22⋊Dic11—42no—
138C22⋊Dic11—42no—
139C22⋊Dic11—41no—
140C22⋊Dic11—81no—
141C22⋊Dic11—81no—
142C22⋊Dic11—81no—
143C22⋊Dic11—81no—
144C22⋊Dic11—82no—
145C22⋊Dic11—82no—
146C4⋊Dic11—41no—
147Dic11⋊C4—42no—
148C4×Dic11—22no—
149C4×Dic11—41no—
150C22×#99D1111yescharacteristic
151#2435—111no—
152C2×#354—112no—
153#1781—111no—
154#1393—112no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—41no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—81no—
187C23×C11—81no—
188C23×C11—81no—
189C23×C11—81no—
190C23×C11—84no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11—84no—
194C23×C11—84no—
195C23×C11#9911yescharacteristic
196C23×C11#9911yescharacteristic
197C23×C11#9912yes—
198C23×C11C2×C22⋊C411yescharacteristic
199C23×C11#12011yescharacteristic
200C23×C11#12112yes—
201C23×C11#12311yescharacteristic
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—44no—
205D4×C11—44no—
206D4×C11—42no—
207D4×C11—42no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—88no—
217C2×C4×C11—82no—
218C2×C4×C11—82no—
219C2×C4×C11C4×D412yes—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—82no—
233C2×Dic11—82no—
234C2×Dic11—82no—
235Dic22—82no—
236C23×D4C2×D1111yescharacteristic
237C2×#124—111no—
238C2×#124—111no—
239C2×C22⋊Q8—111no—
240C22×C22⋊C4—21no—
241C2×#99—21no—
242C2×#99—24no—
243C2×#99—112no—
244C2×#99—221no—
245C2×#99C2×D1112yes—
246#394—221no—
247#394—221no—
248#390—111no—
249#390—111no—
250#379—221no—
251#379—221no—
252#379—221no—
253C4×C22⋊C4—111no—
254#354—224no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—22no—
264C22×C11—21no—
265C22×C11—22no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—41no—
270C22×C11—42no—
271C22×C11—41no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—42no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—84no—
288C22×C11—81no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11—84no—
292C22×C11#35412yescomplemented
293C22×C11#38611yescharacteristic
294C22×C11C2×#9911yescharacteristic
295C22×C11C2×#9911yescharacteristic
296C4×C11—22no—
297C4×C11—41no—
298C4×C11—84no—
299Dic11—81no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303Dic11—162no—
304C25D4411yescharacteristic
305C25C22⋊D1111yescharacteristic
306C22×Q8—111no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—41no—
310C22×D4—41no—
311C22×D4—42no—
312C22×D4C4×D1111yescharacteristic
313C22×D4D4411yescharacteristic
314C22×D4C22⋊D1111yescharacteristic
315C22×D4C22×D1111yescharacteristic
316C23×C4—41no—
317C23×C4C4×D1111yescharacteristic
318#124—222no—
319#124—222no—
320#124—442no—
321C22⋊Q8—441no—
322C22⋊Q8—441no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—221no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—221no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—221no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4—221no—
337C2×C22⋊C4—221no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—221no—
340C2×C22⋊C4—441no—
341C2×C22⋊C4—441no—
342C2×C42—111no—
343C2×C42—111no—
344#99—24no—
345#99—22no—
346#99—222no—
347#99—222no—
348#99—442no—
349#99C22⋊D1114yes—
350#95—221no—
351C2×C11—21no—
352C2×C11—21no—
353C2×C11—22no—
354C2×C11—42no—
355C2×C11—41no—
356C2×C11—41no—
357C2×C11—42no—
358C2×C11—41no—
359C2×C11—81no—
360C2×C11#189811yescharacteristic
361C2×C11C2×#35411yescharacteristic
362C2×C11#212711yescharacteristic
363C24—21no—
364C24—22no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—41no—
372C24—42no—
373C24—42no—
374C24—81no—
375C24—81no—
376C24(C2×D11)⋊C411yescharacteristic
377C24(C2×D11)⋊C411yescharacteristic
378C24(C2×D11)⋊C411yescharacteristic
379C24C2×D4411yescharacteristic
380C24C2×C22⋊D1111yescharacteristic
381C2×Q8—222no—
382C2×Q8—441no—
383C2×Q8—441no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—44no—
400C2×D4#433912yes—
401C2×D4C2×C22⋊D1112yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—41no—
406C22×C4—44no—
407C22×C4—42no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—221no—
413C22×C4—221no—
414C22×C4—442no—
415C22×C4(C2×D11)⋊C411yescharacteristic
416C22×C4C2×C4×D1111yescharacteristic
417C4⋊C4—441no—
418C4⋊C4—442no—
419C22⋊C4—24no—
420C22⋊C4—44no—
421C22⋊C4—42no—
422C22⋊C4—442no—
423C22⋊C4—442no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—442no—
427C22⋊C4—441no—
428C22⋊C4—442no—
429C22⋊C4—441no—
430C22⋊C4—442no—
431C22⋊C4—442no—
432C22⋊C4—881no—
433C22⋊C4—881no—
434C22⋊C4—881no—
435C22⋊C4—881no—
436C22⋊C4—882no—
437C22⋊C4—882no—
438C42—222no—
439C42—441no—
440C11#1309011yescharacteristic, complemented, Sylow
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—22no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—41no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23—84no—
477C23—82no—
478C23—82no—
479C23—84no—
480C23—84no—
481C23#6687011yescharacteristic
482C23#6687011yescharacteristic
483C23#6687012yes—
484C23C2×(C2×D11)⋊C411yescharacteristic
485C23#6698211yescharacteristic
486C23#6698312yes—
487C23#6700611yescharacteristic
488Q8—882no—
489D4—42no—
490D4—42no—
491D4—44no—
492D4—44no—
493D4—42no—
494D4—42no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—88no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—882no—
519C2×C4—882no—
520C2×C4—882no—
521C2×C4C4×C22⋊D1112yes—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—22no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—44no—
540C22—44no—
541C22—42no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—84no—
555C22—81no—
556C22—82no—
557C22—82no—
558C22—84no—
559C22#1062211112yescomplemented
560C22C2×#6687011yescharacteristic
561C22C2×#6687011yescharacteristic
562C22#1062282611yescharacteristic
563C4—22no—
564C4—41no—
565C4—84no—
566C4—881no—
567C4—881no—
568C4—881no—
569C4—881no—
570C4—1762no—
571C2—21no—
572C2—21no—
573C2—22no—
574C2—41no—
575C2—42no—
576C2—41no—
577C2—42no—
578C2—41no—
579C2—81no—
580C2#1306906911yescharacteristic
581C2C2×#1062211111yescharacteristic
582C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC22×C11×#99C2
socleC22×C11C2×#99
prime radicalC23×D4×C11C22
cosocleC22×D4×C11C23
hypercenterC22×#99D11
hypocenterC11#13090
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10622111C2semidirect
4. #13066740C2semidirect
8. C2×#66989C4semidirect
10. C2×#66977C4semidirect
19. #10622834C4semidirect
23. C4×C22⋊Dic11C4semidirect
38. C22×Dic22C2×C4semidirect
59. C2×C4⋊Dic11C2×C4semidirect
63. C2×C4×Dic11C2×C4semidirect
64. C2×C4×Dic11C2×C4semidirect
292. C22×C11#354semidirect
440. C11#13090semidirect
559. C22#10622111semidirect

Maximal subgroups

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

subgroupindex
#130722632
C2×#106221112
#130685312
#130667402
C22×C11×#992
#1309011