Finite Group Databasebeta

← #14753978

Subgroups — #14753978

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622321C211yesmaximal, characteristic
2#13071241C211yesmaximal, characteristic
3#13071237C211yesmaximal, characteristic
4#13068750C211yesmaximal, characteristic, complemented
5#13068748C211yesmaximal, characteristic, complemented
6#13068748C211yesmaximal, characteristic, complemented
7#13068746C211yesmaximal, characteristic, complemented
8#13068745C211yesmaximal, characteristic, complemented
9#13068743C211yesmaximal, characteristic, complemented
10#13068742C211yesmaximal, characteristic, complemented
11#13068334C211yesmaximal, characteristic
12#13068334C211yesmaximal, characteristic
13#13068331C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#1836C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C11×#382C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622602—21no—
29#10622602—21no—
30#10622590C2211yescharacteristic
31#10622590C2211yescharacteristic
32#10622589C2211yescharacteristic
33#10622589C2211yescharacteristic
34#10622585—21no—
35#10622585—21no—
36#10622549C2211yescharacteristic
37#10622548C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622321C418yescomplemented
40#10622281—21no—
41#10622281—21no—
42#10622260—21no—
43#10622260—21no—
44C11×#340C2211yescharacteristic
45C11×#340C2211yescharacteristic
46C11×#340C2211yescharacteristic
47C11×#340C2211yescharacteristic
48#10622189C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4D411yescharacteristic
89C2×Dic11⋊C4D411yescharacteristic
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313C2×C414yes—
98C2×C8×D11—22no—
99C2×C8×D11—22no—
100C2×C8×D11C2×C414yes—
101#66945—22no—
102#66945—22no—
103#66945—22no—
104#66945—22no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—22no—
109#66925C2×C414yes—
110#66925Q814yes—
111C11×#97C2×C414yescomplemented
112C11×#95—21no—
113C11×#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66879C2×C414yescomplemented
121C8×Dic11C2×C414yescomplemented
122C4×C11⋊C8C2×C414yescomplemented
123#20763—111nomaximal, Sylow
124C23×D11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×C4×D11—81no—
142C2×C4×D11—81no—
143C2×C4×D11—81no—
144C2×C4×D11—81no—
145C2×C4×D11C22×C412yes—
146C2×C4×D11C2×Q812yes—
147C2×C4×D11#4112yes—
148C2×C4×D11#4112yes—
149C2×C4×D11#4112yes—
150C2×C4×D11#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C22×C412yes—
156C2×C8×C11C22×C412yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4—81no—
167C42×C11C22×C412yes—
168C42×C11C2×Q812yes—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4C4⋊C414yes—
172(C2×D11)⋊C4C4⋊C414yes—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—81no—
182C4⋊Dic11—81no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185Dic11⋊C4—81no—
186Dic11⋊C4—81no—
187Dic11⋊C4—81no—
188Dic11⋊C4—81no—
189Dic11⋊C4C4⋊C414yes—
190Dic11⋊C4C4⋊C414yes—
191C4×Dic11—42no—
192C4×Dic11—42no—
193C4×Dic11C22×C412yes—
194C4×Dic11C2×Q812yes—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C412yes—
200C2×C11⋊C8C22×C412yes—
201#4313—28no—
202C8×D11—28no—
203C2×#405—111no—
204#2317—111no—
205#2317—111no—
206#1836—111no—
207#1836—111no—
208#1836—111no—
209#1836D1111yescharacteristic, complemented
210#1835—111no—
211#1835—111no—
212#1834—111no—
213#1834—111no—
214#1736—111no—
215#1736—111no—
216#1735—111no—
217C2×#340—111no—
218C23×C11C22×D411yescharacteristic
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11C2×C4⋊C412yes—
224C22×D11#12412yes—
225C22×D11#12412yes—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C2×C4⋊C412yes—
243C2×C4×C11C2×C4⋊C412yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×Q811yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11C2×C4⋊C412yes—
267C2×Dic11C2×C4⋊C412yes—
268C2×Dic11C2×C4⋊C412yes—
269C2×Dic11#12412yes—
270C2×Dic11#12412yes—
271C4×D11—84no—
272C4×D11—84no—
273C4×D11#11714yes—
274C4×D11#11714yes—
275C4×D11#12514yes—
276C4×D11#12514yes—
277C8×C11—22no—
278C8×C11—22no—
279C11⋊C8—22no—
280C11⋊C8—22no—
281C22×M16—111no—
282C23×C8—111no—
283C2×#117—111no—
284C2×#117—111no—
285C2×#117—111no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288#405—118no—
289C2×#97—111no—
290C2×#97C2×D1111yescharacteristic
291C2×C4×C8—111no—
292C2×C4×C8—111no—
293#389—221no—
294#389—221no—
295#389—221no—
296#389—221no—
297#385—221no—
298#385—221no—
299#385—221no—
300#385—221no—
301#384—111no—
302#384—111no—
303#384—111no—
304#384C2×D1111yescharacteristic
305#382—111no—
306#382—111no—
307#382—111no—
308#382C2×D1111yescharacteristic
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340C2×D1111yescharacteristic
322#340C2×D1111yescharacteristic
323#340C2×D1111yescharacteristic
324#340C2×D1111yescharacteristic
325C22×C11C22×C4⋊C411yescharacteristic
326C22×C11C2×#12411yescharacteristic
327C22×C11C2×#12411yescharacteristic
328C22×C11#57611yescharacteristic
329C22×C11#57711yescharacteristic
330C22×C11#57711yescharacteristic
331C22×C11#57811yescharacteristic
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—22no—
338C2×D11#38214yes—
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C2×#11711yescharacteristic
346C4×C11C2×#11711yescharacteristic
347C4×C11C2×#12511yescharacteristic
348C4×C11C2×#12511yescharacteristic
349Dic11—22no—
350Dic11—22no—
351Dic11—81no—
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355Dic11#38214yes—
356C23×C4—111no—
357C23×C4—221no—
358C23×C4—221no—
359C2×M16—114no—
360C2×M16—222no—
361C2×M16—222no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8—114no—
365C22×C8—222no—
366C22×C8—222no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369#117—114no—
370#117—114no—
371#117—222no—
372#117—222no—
373#117—222no—
374#117—222no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C22⋊C4—111no—
400C2×C22⋊C4—111no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C42—111no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407#97—114no—
408#97C4×D1114yescomplemented
409C4×C8—114no—
410C4×C8—114no—
411#95—21no—
412#95—21no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419C2×C11C2×#38211yescharacteristic
420C2×C11#291211yescharacteristic
421C2×C11#291311yescharacteristic
422C2×C11#313611yescharacteristic
423C2×C11#313611yescharacteristic
424C2×C11#313711yescharacteristic
425C2×C11#313711yescharacteristic
426D11—24no—
427C24—111no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—111no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—881no—
448C22×C4—881no—
449C22×C4—881no—
450C22×C4—881no—
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454M16—228no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—112no—
460C2×C8—112no—
461C2×C8—228no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8C2×C4×D1112yes—
467C2×C8C2×C4×D1112yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—114no—
479C4⋊C4—114no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4—881no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4—881no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C22⋊C4—114no—
497C22⋊C4—114no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—112no—
501C42—112no—
502C42—442no—
503C42—442no—
504C42C2×C4×D1112yes—
505C42Q8×D1112yes—
506C11#2076311yescharacteristic, complemented, Sylow
507C23—112no—
508C23—112no—
509C23—112no—
510C23—221no—
511C23—221no—
512C23—221no—
513C23—221no—
514C23C2×D4×D1111yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—112no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—114no—
535C2×C4—114no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—884no—
557C2×C4—884no—
558C2×C4C4⋊C4×D1112yes—
559C2×C4C4⋊C4×D1112yes—
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×Q8×D1111yescharacteristic
562C2×C4#41×D1111yescharacteristic
563C2×C4#41×D1111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#41×D1111yescharacteristic
566C8—22no—
567C8—22no—
568C8—222no—
569C8—222no—
570C22—114no—
571C22—222no—
572C22—222no—
573C22—222no—
574C22—222no—
575C22—222no—
576C22—222no—
577C22C2×C4⋊C4×D1111yescharacteristic
578C22D11×#12411yescharacteristic
579C22D11×#12411yescharacteristic
580C22#1062330511yescharacteristic
581C22#1062330611yescharacteristic
582C22#1062330911yescharacteristic
583C22#1062331011yescharacteristic
584C4—22no—
585C4—22no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—114no—
591C4—222no—
592C4—222no—
593C4—881no—
594C4—881no—
595C4—881no—
596C4—881no—
597C4D11×#11711yescharacteristic
598C4D11×#11711yescharacteristic
599C4D11×#12511yescharacteristic
600C4D11×#12511yescharacteristic
601C2—224no—
602C2D11×#38211yescharacteristic
603C2#1307721011yescharacteristic
604C2#1307721511yescharacteristic
605C2#1307896711yescharacteristic
606C2#1307897111yescharacteristic
607C2#1307897811yescharacteristic
608C2#1307898211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1836C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1836D11
hypocenterC11#20763
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #13068750C2semidirect
5. #13068748C2semidirect
6. #13068748C2semidirect
7. #13068746C2semidirect
8. #13068745C2semidirect
9. #13068743C2semidirect
10. #13068742C2semidirect
15. C11×#1836C2semidirect
39. #10622321C4semidirect
111. C11×#97C2×C4semidirect
120. #66879C2×C4semidirect
121. C8×Dic11C2×C4semidirect
122. C4×C11⋊C8C2×C4semidirect
209. #1836D11semidirect
408. #97C4×D11semidirect
506. C11#20763semidirect

Maximal subgroups

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

subgroupindex
C2×#106223212
#130712412
#130712372
#130687502
#130687482
#130687462
#130687452
#130687432
#130687422
#130683342
#130683312
D11×#3402
C11×#18362
#2076311