Finite Group Databasebeta

← #14671272

Subgroups — #14671272

Order 2816.

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

normal subgroups only

This group has 894 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#13071939C211yesmaximal, characteristic
2C2×#10622110C212yesmaximal, complemented
3#13068537C211yesmaximal, characteristic
4#13066733C212yesmaximal, complemented
5C22×C11×#99C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C22×C11×C22⋊C4—21no—
8C22×C22⋊Dic11C411yescharacteristic, complemented
9C2×#66988C411yescharacteristic, complemented
10C2×#66988C2211yescharacteristic
11C2×C11×#99—21no—
12C2×C11×#99—24no—
13C2×C11×#99C2212yes—
14#10622860—21no—
15#10622860C411yescharacteristic, complemented
16#10622835—21no—
17#10622835—21no—
18#10622833C411yescharacteristic, complemented
19#10622833C2211yescharacteristic
20C2×#66897—21no—
21C2×#66897C2212yes—
22#10622823—21no—
23#10622820—21no—
24#10622110—24no—
25C25×C11C2×C411yescharacteristic
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×C11D411yescharacteristic
38C23×Dic11C2×C411yescharacteristic, complemented
39C23×Dic11C2×C411yescharacteristic, complemented
40C2×C11×C22⋊C4—24no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—41no—
43C2×C11×C22⋊C4—42no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—41no—
53C2×C22⋊Dic11—41no—
54C2×C22⋊Dic11C2×C411yescharacteristic, complemented
55C2×C22⋊Dic11C2×C411yescharacteristic, complemented
56#66988—22no—
57#66988—22no—
58#66988—42no—
59C2×Dic11⋊C4—21no—
60C2×Dic11⋊C4—21no—
61C2×#4318—22no—
62C11×#99—24no—
63C11×#99—22no—
64C11×#99D414yes—
65#66897—22no—
66#66897—22no—
67#66897—42no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)—41no—
71C22⋊(C11⋊C8)—41no—
72#13084—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×C11C22×C411yescharacteristic
90C24×C11C2×D411yescharacteristic
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—21no—
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×C11C2×D411yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11—81no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—44no—
130C11×C22⋊C4—42no—
131C22⋊Dic11—22no—
132C22⋊Dic11—41no—
133C22⋊Dic11—42no—
134C22⋊Dic11—42no—
135C22⋊Dic11—42no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—81no—
141C22⋊Dic11—81no—
142C22⋊Dic11—81no—
143Dic11⋊C4—42no—
144Dic11⋊C4—42no—
145#4318—42no—
146#4318—42no—
147C2×C11⋊C8—42no—
148C22×#99D1111yescharacteristic
149#2405—111no—
150C2×#352—112no—
151#1783—111no—
152#1390—112no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—21no—
159C23×C11—21no—
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—41no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—42no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—81no—
185C23×C11—81no—
186C23×C11—81no—
187C23×C11—81no—
188C23×C11—84no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11—84no—
192C23×C11—84no—
193C23×C11#9911yescharacteristic
194C23×C11#9911yescharacteristic
195C23×C11#9912yes—
196C23×C11C2×C22⋊C411yescharacteristic
197C23×C11C4×D412yes—
198C23×C11#12011yescharacteristic
199C23×C11#12311yescharacteristic
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—42no—
205D4×C11—42no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11—88no—
215C2×C4×C11—82no—
216C2×C4×C11—82no—
217C2×C4×C11#12112yes—
218C2×Dic11—41no—
219C2×Dic11—41no—
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—82no—
231C2×Dic11—82no—
232C11⋊C8—82no—
233C23×D4C2×D1111yescharacteristic
234C2×#123—111no—
235C2×#123—111no—
236C22×C22⋊C4—21no—
237C22×C22⋊C4—111no—
238C2×#100—112no—
239C2×#100—221no—
240C2×#99—21no—
241C2×#99—24no—
242C2×#99C2×D1112yes—
243#407—221no—
244#394—221no—
245#394—221no—
246#386—111no—
247#386—111no—
248#385—221no—
249#379—111no—
250#379—221no—
251#352—224no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—22no—
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—44no—
270C22×C11—42no—
271C22×C11—44no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—84no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—84no—
289C22×C11#35212yescomplemented
290C22×C11#38611yescharacteristic
291C22×C11C2×#9911yescharacteristic
292C22×C11C2×#9911yescharacteristic
293C4×C11—22no—
294C4×C11—41no—
295C4×C11—84no—
296Dic11—81no—
297Dic11—81no—
298Dic11—81no—
299Dic11—81no—
300C25C4×D1111yescharacteristic
301C25C22⋊D1111yescharacteristic
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—41no—
305C22×D4—41no—
306C22×D4—42no—
307C22×D4C4×D1111yescharacteristic
308C22×D4D4411yescharacteristic
309C22×D4C22⋊D1111yescharacteristic
310C22×D4C22×D1111yescharacteristic
311C23×C4—41no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4D4411yescharacteristic
315C2×M16—222no—
316#123—222no—
317#123—222no—
318#123—442no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—111no—
326C2×C22⋊C4—111no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
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—441no—
336C2×C22⋊C4—441no—
337#100—222no—
338#100—222no—
339#100—442no—
340#99—24no—
341#99—22no—
342#99C22⋊D1114yes—
343C22⋊C8—441no—
344C22⋊C8—441no—
345#95—221no—
346#95—221no—
347C2×C11—21no—
348C2×C11—21no—
349C2×C11—22no—
350C2×C11—41no—
351C2×C11—41no—
352C2×C11—42no—
353C2×C11—41no—
354C2×C11—42no—
355C2×C11—81no—
356C2×C11#189811yescharacteristic
357C2×C11C2×#35211yescharacteristic
358C2×C11#212111yescharacteristic
359C24—21no—
360C24—22no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—22no—
367C24—41no—
368C24—42no—
369C24—42no—
370C24—81no—
371C24—81no—
372C24(C2×D11)⋊C411yescharacteristic
373C24(C2×D11)⋊C411yescharacteristic
374C24(C2×D11)⋊C411yescharacteristic
375C24C2×C4×D1111yescharacteristic
376C24C2×C22⋊D1111yescharacteristic
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4#433912yes—
394C2×D4C2×C22⋊D1112yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—41no—
399C22×C4—44no—
400C22×C4—42no—
401C22×C4—82no—
402C22×C4—82no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—222no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4—441no—
411C22×C4—881no—
412C22×C4(C2×D11)⋊C411yescharacteristic
413C22×C4C2×D4411yescharacteristic
414M16—442no—
415M16—442no—
416C2×C8—442no—
417C4⋊C4—442no—
418C4⋊C4—442no—
419C22⋊C4—24no—
420C22⋊C4—44no—
421C22⋊C4—42no—
422C22⋊C4—222no—
423C22⋊C4—442no—
424C22⋊C4—442no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—442no—
428C22⋊C4—441no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C22⋊C4—881no—
432C22⋊C4—881no—
433C22⋊C4—881no—
434C11#1308411yescharacteristic, complemented, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—41no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—81no—
467C23—81no—
468C23—81no—
469C23—81no—
470C23—84no—
471C23—82no—
472C23—82no—
473C23—84no—
474C23—84no—
475C23#6687011yescharacteristic
476C23#6687011yescharacteristic
477C23#6687012yes—
478C23C2×(C2×D11)⋊C411yescharacteristic
479C23C4×C22⋊D1112yes—
480C23#6698211yescharacteristic
481C23#6700611yescharacteristic
482D4—42no—
483D4—42no—
484D4—44no—
485D4—44no—
486D4—42no—
487D4—42no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—88no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—882no—
512C2×C4—882no—
513C2×C4#6698312yes—
514C8—882no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—22no—
522C22—22no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—41no—
531C22—41no—
532C22—44no—
533C22—42no—
534C22—44no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—84no—
547C22—81no—
548C22—81no—
549C22—82no—
550C22—82no—
551C22—84no—
552C22#1062211012yescomplemented
553C22C2×#6687011yescharacteristic
554C22C2×#6687011yescharacteristic
555C22#1062282611yescharacteristic
556C4—22no—
557C4—41no—
558C4—84no—
559C4—881no—
560C4—881no—
561C4—881no—
562C4—881no—
563C2—21no—
564C2—21no—
565C2—22no—
566C2—41no—
567C2—41no—
568C2—42no—
569C2—41no—
570C2—42no—
571C2—81no—
572C2#1306906911yescharacteristic
573C2C2×#1062211011yescharacteristic
574C2#1307026011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC22×C11×#99C2
socleC22×C11C2×#99
prime radicalC23×D4×C11C22
cosocleC22×D4×C11C23
hypercenterC22×#99D11
hypocenterC11#13084
LCSG ▷ C24×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×#10622110C2semidirect
4. #13066733C2semidirect
8. C22×C22⋊Dic11C4semidirect
9. C2×#66988C4semidirect
15. #10622860C4semidirect
18. #10622833C4semidirect
38. C23×Dic11C2×C4semidirect
39. C23×Dic11C2×C4semidirect
54. C2×C22⋊Dic11C2×C4semidirect
55. C2×C22⋊Dic11C2×C4semidirect
289. C22×C11#352semidirect
434. C11#13084semidirect
552. C22#10622110semidirect

Maximal subgroups

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

subgroupindex
#130719392
C2×#106221102
#130685372
#130667332
C22×C11×#992
#1308411