Finite Group Databasebeta

← #14671270

Subgroups — #14671270

Order 2816.

894 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C22×#66898C211yesmaximal, characteristic
2#13071939C211yesmaximal, characteristic
3C2×#10622114C212yesmaximal, complemented
4#13066735C212yesmaximal, complemented
5C11×#1783C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C22×C22⋊Dic11—21no—
8C22×C22⋊Dic11C411yescharacteristic, complemented
9C2×#66988C411yescharacteristic, complemented
10C2×#66988C2211yescharacteristic
11C2×C11×#100—21no—
12C2×C11×#100C2212yes—
13C11×#407—21no—
14#10622860—21no—
15#10622860C411yescharacteristic, complemented
16#10622835—21no—
17#10622835—21no—
18#10622833C411yescharacteristic, complemented
19#10622833C2211yescharacteristic
20C2×#66898—21no—
21C2×#66898—24no—
22C2×#66898C2212yes—
23#10622823—21no—
24#10622114—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×C11D411yescharacteristic
37C23×Dic11—41no—
38C23×Dic11C2×C411yescharacteristic, complemented
39C23×Dic11C2×C411yescharacteristic, complemented
40C2×C11×M16—22no—
41C2×C22⋊Dic11—24no—
42C2×C22⋊Dic11—22no—
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—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—41no—
52C2×C22⋊Dic11—42no—
53C2×C22⋊Dic11—41no—
54C2×C22⋊Dic11—41no—
55C2×C22⋊Dic11C2×C411yescharacteristic, complemented
56C2×C22⋊Dic11C2×C411yescharacteristic, complemented
57#66988—22no—
58#66988—22no—
59#66988—42no—
60C2×Dic11⋊C4—21no—
61C2×Dic11⋊C4—21no—
62C11×#100—22no—
63C11×#100—22no—
64C11×#100—42no—
65C11×C22⋊C8—41no—
66C11×C22⋊C8—41no—
67#66898—24no—
68#66898—22no—
69#66898D414yes—
70C11⋊#95—21no—
71C11⋊#95—21no—
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×C11C22⋊C411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11—44no—
121C22×Dic11—42no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—81no—
126C22×Dic11—82no—
127C22×Dic11—82no—
128C11×M16—42no—
129C11×M16—42no—
130C2×C8×C11—42no—
131C22⋊Dic11—22no—
132C22⋊Dic11—24no—
133C22⋊Dic11—41no—
134C22⋊Dic11—42no—
135C22⋊Dic11—44no—
136C22⋊Dic11—42no—
137C22⋊Dic11—42no—
138C22⋊Dic11—42no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—81no—
144C22⋊Dic11—81no—
145C22⋊Dic11—81no—
146Dic11⋊C4—42no—
147Dic11⋊C4—42no—
148C22×#99—111no—
149#2405—111no—
150C2×#352—112no—
151#1783D1111yescharacteristic
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#12112yes—
214C2×Dic11—44no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
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—88no—
228C2×Dic11—82no—
229C2×Dic11—82no—
230C2×Dic11—82no—
231C2×Dic11—82no—
232C8×C11—82no—
233C23×D4C2×D1111yescharacteristic
234C2×#123—111no—
235C2×#123—111no—
236C22×C22⋊C4—111no—
237C22×C22⋊C4—221no—
238C2×#100—21no—
239C2×#100C2×D1112yes—
240C2×#99—112no—
241C2×#99—224no—
242C2×#99—221no—
243#407—21no—
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—22no—
260C22×C11—21no—
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—42no—
270C22×C11—44no—
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—
295Dic11—81no—
296Dic11—81no—
297Dic11—84no—
298Dic11—81no—
299Dic11—81no—
300C25C4×D1111yescharacteristic
301C25D4411yescharacteristic
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—111no—
312C23×C4—111no—
313C23×C4—441no—
314C23×C4C22⋊D1111yescharacteristic
315C2×M16—22no—
316#123—222no—
317#123—222no—
318#123—442no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C22⋊C4—111no—
322C2×C22⋊C4—111no—
323C2×C22⋊C4—224no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
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—441no—
334C2×C22⋊C4—442no—
335C2×C22⋊C4—441no—
336C2×C22⋊C4—441no—
337#100—22no—
338#100—22no—
339#100—42no—
340#99—114no—
341#99—224no—
342#99—222no—
343C22⋊C8—41no—
344C22⋊C8—41no—
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×D4411yescharacteristic
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×D4D4×D1112yes—
394C2×D4#434112yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—41no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4—444no—
405C22×C4—442no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4—881no—
410C22×C4—882no—
411C22×C4—882no—
412C22×C4(C2×D11)⋊C411yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414M16—42no—
415M16—42no—
416C2×C8—42no—
417C4⋊C4—442no—
418C4⋊C4—442no—
419C22⋊C4—222no—
420C22⋊C4—224no—
421C22⋊C4—444no—
422C22⋊C4—442no—
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—
478C23(C22⋊D11)⋊C412yes—
479C23#6693511yescharacteristic
480C23#6693911yescharacteristic
481C23C2×(C2×D11)⋊C411yescharacteristic
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—444no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
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—888no—
509C2×C4—882no—
510C2×C4—882no—
511C2×C4—882no—
512C2×C4—882no—
513C2×C4#6699212yes—
514C8—82no—
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#1062211412yescomplemented
553C22C2×#6687011yescharacteristic
554C22C2×#6687011yescharacteristic
555C22#1062257111yescharacteristic
556C4—22no—
557C4—41no—
558C4—881no—
559C4—881no—
560C4—884no—
561C4—881no—
562C4—881no—
563C2—21no—
564C2—21no—
565C2—22no—
566C2—41no—
567C2—41no—
568C2—42no—
569C2—41no—
570C2—42no—
571C2—81no—
572C2#1306906711yescharacteristic
573C2C2×#1062211411yescharacteristic
574C2#1307026311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1783C2
socleC22×C11C2×#99
prime radicalC23×D4×C11C22
cosocleC22×D4×C11C23
hypercenter#1783D11
hypocenterC11#13084
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #1783

Complements

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

NH ≅ G/Ntype
3. C2×#10622114C2semidirect
4. #13066735C2semidirect
8. C22×C22⋊Dic11C4semidirect
9. C2×#66988C4semidirect
15. #10622860C4semidirect
18. #10622833C4semidirect
38. C23×Dic11C2×C4semidirect
39. C23×Dic11C2×C4semidirect
55. C2×C22⋊Dic11C2×C4semidirect
56. C2×C22⋊Dic11C2×C4semidirect
289. C22×C11#352semidirect
434. C11#13084semidirect
552. C22#10622114semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
#130719392
C2×#106221142
#130667352
C11×#17832
#1308411