Finite Group Databasebeta

← #14814377

Subgroups — #14814377

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072063C211yesmaximal, characteristic
2C4⋊C4×C22⋊D11C211yesmaximal, characteristic
3#13070177C211yesmaximal, characteristic, complemented
4#13070049C211yesmaximal, characteristic, complemented
5#13070027C211yesmaximal, characteristic, complemented
6#13069809C211yesmaximal, characteristic, complemented
7#13069252C211yesmaximal, characteristic, complemented
8#13069204C211yesmaximal, characteristic, complemented
9#13069036C211yesmaximal, characteristic, complemented
10#13068920C211yesmaximal, characteristic, complemented
11#13068905C211yesmaximal, characteristic
12#13068810C211yesmaximal, characteristic, complemented
13#13068702C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×C4×C22⋊D11—21no—
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622823—21no—
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36#10622602—21no—
37#10622600—21no—
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622593—21no—
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622585—21no—
44C2×#66872C2211yescharacteristic
45#10622569—21no—
46#10622561—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11D411yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—41no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81#66999—22no—
82#66999—22no—
83C4×C22⋊D11—22no—
84C4×C22⋊D11—22no—
85C4×C22⋊D11—44no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×C8×D11—22no—
105C2×C8×D11—41no—
106C2×C8×D11—41no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—41no—
110C4⋊C4×D11—41no—
111C11×#103—22no—
112C11×#103—41no—
113C11×C22⋊C8—41no—
114#66899—41no—
115#66899—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C22⋊(C11⋊C8)—41no—
124(C2×D11)⋊C8—22no—
125#66881—41no—
126#66872—22no—
127#26200—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11C2×D411yescharacteristic
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—22no—
152C2×C22⋊D11—22no—
153C2×C22⋊D11SD1614yes—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C4×D11#4112yes—
172C2×C4×D11#4112yes—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4#4112yes—
186C11×C4⋊C4#4112yes—
187C11×C22⋊C4—42no—
188C22⋊Dic11—22no—
189C22⋊Dic11—42no—
190C22⋊Dic11—81no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—81no—
203Dic11⋊C4—22no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—81no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C8×D11—44no—
219#2417—111no—
220D4×C4⋊C4—111no—
221#2099—111no—
222#2077—111no—
223#2072—111no—
224#2035—111no—
225#1927—111no—
226#1920—111no—
227#1892—111no—
228#1872—111no—
229#1872D1111yescharacteristic, complemented
230#1869—111no—
231#1853—111no—
232#1823—111no—
233C2×#340—111no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11C2×SD1612yes—
241C23×C11C22×D411yescharacteristic
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11#12312yes—
247C22×D11C2×SD1612yes—
248C22×D11#13712yes—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—84no—
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C22⋊D11—28no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11#12312yes—
300C2×Dic11C2×SD1612yes—
301C4×D11—22no—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—84no—
306C4×D11—84no—
307C8×C11—41no—
308C8×C11—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C23×C8—111no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8C2×D1111yescharacteristic
314C2×C4×D4—111no—
315C2×C4×D4—221no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318C22×C4⋊C4C2×D1111yescharacteristic
319C2×#106—111no—
320C2×#106—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103C2×D1111yescharacteristic
324C2×#103C2×D1111yescharacteristic
325C2×C22⋊C8—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328#398—221no—
329#396—221no—
330#391—111no—
331#389—111no—
332#389—221no—
333#386—221no—
334#385—221no—
335#385—221no—
336#384—111no—
337#380—111no—
338#380—111no—
339#380—111no—
340#380—221no—
341C4×C4⋊C4—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340C2×D1111yescharacteristic
351#340C2×D1111yescharacteristic
352#336—111no—
353#336—111no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11C2×#12311yescharacteristic
362C22×C11#54611yescharacteristic
363C22×C11#54611yescharacteristic
364C22×C11C22×SD1611yescharacteristic
365C22×C11C2×#13711yescharacteristic
366C22×C11#57611yescharacteristic
367C22×C11#57811yescharacteristic
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11#48314yes—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11#52911yescharacteristic
381C4×C11#53811yescharacteristic
382C4×C11#55311yescharacteristic
383C4×C11#55311yescharacteristic
384Dic11—22no—
385Dic11—22no—
386Dic11—41no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8C22×D1111yescharacteristic
392C22×D4—111no—
393C23×C4—21no—
394C23×C4—111no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4C22×D1111yescharacteristic
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—222no—
401C22×C8—441no—
402C22×C8—441no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C22⋊Q8—22no—
406C22⋊Q8—41no—
407C22⋊Q8—222no—
408C22⋊Q8—222no—
409C4×D4—222no—
410C4×D4—222no—
411C4×D4—444no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—222no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—441no—
430C2×C4⋊C4—441no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—111no—
442C2×C42—221no—
443#106—222no—
444#106—441no—
445#103—22no—
446#103—41no—
447#103—441no—
448#103—441no—
449C22⋊C8—41no—
450C22⋊C8—222no—
451C22⋊C8—441no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11—42no—
460C2×C11#244411yescharacteristic
461C2×C11C2×#48311yescharacteristic
462C2×C11#309811yescharacteristic
463C2×C11#329511yescharacteristic
464C2×C11#329811yescharacteristic
465C2×C11#331211yescharacteristic
466C2×C11#331411yescharacteristic
467D11—24no—
468C24—111no—
469C24D4×D1111yescharacteristic
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×D4—114no—
477C2×D4—222no—
478C2×D4—222no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—81no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—111no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4—881no—
510C22×C4—881no—
511C22×C4D4×D1111yescharacteristic
512C22×C4C23×D1111yescharacteristic
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—444no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—222no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—881no—
546C4⋊C4—881no—
547C4⋊C4#433912yes—
548C4⋊C4#434112yes—
549C22⋊C4—42no—
550C22⋊C4—222no—
551C22⋊C4—222no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—881no—
556C42—221no—
557C42—221no—
558C42—442no—
559C11#2620011yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—112no—
567C23—112no—
568C23—112no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23SD16×D1112yes—
574C23C2×D4×D1111yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—228no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—884no—
626C2×C4—884no—
627C2×C4C2×#433911yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6703711yescharacteristic
630C2×C4#6703711yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C8—41no—
634C8—41no—
635C8—441no—
636C8—441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—114no—
645C22—222no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—222no—
650C22—222no—
651C22#1062302111yescharacteristic
652C22#1062312211yescharacteristic
653C22D11×#12311yescharacteristic
654C22C2×SD16×D1111yescharacteristic
655C22#1062329711yescharacteristic
656C22#1062330511yescharacteristic
657C22D11×#13711yescharacteristic
658C4—42no—
659C4—42no—
660C4—41no—
661C4—81no—
662C4—81no—
663C4—222no—
664C4—222no—
665C4—441no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4#1062308811yescharacteristic
671C4#1062308911yescharacteristic
672C4#1062314411yescharacteristic
673C4#1062314511yescharacteristic
674C2—42no—
675C2—224no—
676C2#1307236311yescharacteristic
677C2D11×#48311yescharacteristic
678C2#1307859511yescharacteristic
679C2#1308043311yescharacteristic
680C2#1308047711yescharacteristic
681C2#1308066011yescharacteristic
682C2#1308069811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#1872D11
hypocenterC11#26200
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. #13070177C2semidirect
4. #13070049C2semidirect
5. #13070027C2semidirect
6. #13069809C2semidirect
7. #13069252C2semidirect
8. #13069204C2semidirect
9. #13069036C2semidirect
10. #13068920C2semidirect
12. #13068810C2semidirect
13. #13068702C2semidirect
14. D11×#340C2semidirect
15. C11×#1872C2semidirect
229. #1872D11semidirect
559. C11#26200semidirect

Maximal subgroups

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

subgroupindex
#130720632
C4⋊C4×C22⋊D112
#130701772
#130700492
#130700272
#130698092
#130692522
#130692042
#130690362
#130689202
#130689052
#130688102
#130687022
D11×#3402
C11×#18722
#2620011