Finite Group Databasebeta

← #14760921

Subgroups — #14760921

Order 2816.

972 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622350C211yesmaximal, characteristic
2#13071122C211yesmaximal, characteristic
3#117×Dic11C211yesmaximal, characteristic, complemented
4#13069242C211yesmaximal, characteristic, complemented
5#13069235C211yesmaximal, characteristic, complemented
6#13069207C211yesmaximal, characteristic, complemented
7#13069200C211yesmaximal, characteristic, complemented
8#13068938C211yesmaximal, characteristic
9#13068708C211yesmaximal, characteristic, complemented
10#107×Dic11C211yesmaximal, characteristic, complemented
11#106×Dic11C211yesmaximal, characteristic, complemented
12#13068430C211yesmaximal, characteristic, complemented
13#13068430C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×(C22⋊D11)⋊C4—21no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622601C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42#10622571—21no—
43C22⋊C4×Dic11—21no—
44C22⋊C4×Dic11—21no—
45#10622545—21no—
46C42×Dic11—21no—
47#10622350C418yescomplemented
48#10622282—21no—
49#10622279—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11D411yescharacteristic
63C23×Dic11D411yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#117—22no—
69C11×#117—22no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—21no—
78#66983—22no—
79#66983C2×C414yes—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84#66979—22no—
85#66979C2×C414yescomplemented
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66946—22no—
105#66946—22no—
106(C22⋊D11)⋊C4—44no—
107C11×#107—22no—
108C11×#106—22no—
109C11×C22⋊C8C2×C414yescomplemented
110C11×#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118#66885C2×C414yescomplemented
119#66885C2×C414yescomplemented
120#66882C2×C414yescomplemented
121#66881C2×C414yescomplemented
122C8×Dic11—22no—
123C8×Dic11—22no—
124#66873—22no—
125#66873—22no—
126C4×#482—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—24no—
142C2×C22⋊D11—42no—
143C2×C22⋊D11—42no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—41no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44C22×C412yes—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C22×C412yes—
171C2×C8×C11C22×C412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4#4112yes—
179C11×C4⋊C4#4112yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—42no—
182C42×C11—24no—
183C22⋊Dic11—24no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C412yes—
192C4⋊Dic11C22×C412yes—
193C4⋊Dic11C22×C412yes—
194Dic11⋊C4—42no—
195C4×Dic11—22no—
196C4×Dic11—22no—
197C4×Dic11—24no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C4×Dic11#4112yes—
206C4×Dic11#4112yes—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×#482—111no—
214C4×#121—111no—
215C4×#117—111no—
216#1926—111no—
217#1925—111no—
218#1921—111no—
219#1920—111no—
220#1875—111no—
221#1854D1111yescharacteristic, complemented
222#1825—111no—
223C4×#107—111no—
224C4×#106—111no—
225C4×#102—111no—
226C4×#102—111no—
227C4×C22⋊C8—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11C4×D412yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C4×D412yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C22⋊D11—48no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—44no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—44no—
287C2×Dic11#12312yes—
288C2×Dic11#12312yes—
289C2×Dic11#13512yes—
290C2×Dic11#13512yes—
291C2×Dic11AGL(1,ℤ/8)12yes—
292D44—22no—
293D44—22no—
294D44—41no—
295D44—41no—
296C4×D11—84no—
297C8×C11—22no—
298C8×C11—22no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C2×#121—111no—
302C2×C4×D4—111no—
303C2×C4×D4—221no—
304C2×#117—111no—
305C2×#117C2×D1111yescharacteristic
306C22×C42—111no—
307#482—118no—
308C2×#107—111no—
309C2×#107C2×D1111yescharacteristic
310C2×#106—111no—
311C2×#106C2×D1111yescharacteristic
312C2×#102—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×C4×C8—111no—
319C2×C4×C8—111no—
320#390—111no—
321#389—111no—
322#388—221no—
323#386—221no—
324#380C2×D1111yescharacteristic
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—111no—
330C4×C22⋊C4—221no—
331C4×C22⋊C4—221no—
332C4×C22⋊C4—221no—
333#376—221no—
334C43—221no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340C2×D1111yescharacteristic
342#340C2×D1111yescharacteristic
343#336—111no—
344#336—111no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11C2×C4×D411yescharacteristic
353C22×C11C2×#12311yescharacteristic
354C22×C11#52511yescharacteristic
355C22×C11C2×#13511yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C11#57511yescharacteristic
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C4×C11—22no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11C4×#4111yescharacteristic
372C4×C11C4×#4111yescharacteristic
373C4×C11#52911yescharacteristic
374C4×C11#52911yescharacteristic
375Dic11—22no—
376Dic11—22no—
377Dic11—41no—
378Dic11—42no—
379Dic11—42no—
380Dic11—42no—
381Dic11#48214yescomplemented
382C22×D4—111no—
383C22×D4—221no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392#121—114no—
393#121—222no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4—444no—
397#117—22no—
398#117—22no—
399#117—114no—
400#117—222no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C42—21no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—222no—
422C2×C42—222no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429#107—22no—
430#107—114no—
431#106—22no—
432#106—114no—
433#102—114no—
434#102—114no—
435#102—222no—
436#102—222no—
437C22⋊C8—222no—
438C22⋊C8C4×D1114yescomplemented
439C4×C8—222no—
440C4×C8—222no—
441#95—21no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11—42no—
449C2×C11C4×#12311yescharacteristic
450C2×C11C4×#13511yescharacteristic
451C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
452C2×C11C2×#48211yescharacteristic
453C2×C11#309111yescharacteristic
454C2×C11#310211yescharacteristic
455C2×C11#310611yescharacteristic
456D11—82no—
457C24—221no—
458C24D4×D1111yescharacteristic
459C2×D4—112no—
460C2×D4—224no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—442no—
467C2×D4—442no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—441no—
492C22×C4C2×C4×D1112yes—
493C22×C4D4×D1111yescharacteristic
494C22×C4#434312yes—
495C22×C4C23×D1111yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8C2×C4×D1112yes—
507C2×C8C2×C4×D1112yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—112no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—442no—
521C4⋊C4#434112yes—
522C4⋊C4#434112yes—
523C22⋊C4—24no—
524C22⋊C4—42no—
525C22⋊C4—224no—
526C22⋊C4—224no—
527C22⋊C4—442no—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C42—24no—
531C42—112no—
532C42—112no—
533C42—222no—
534C42—222no—
535C42—224no—
536C42—221no—
537C42—221no—
538C42—442no—
539C42—442no—
540C42—442no—
541C42—442no—
542C42—442no—
543C11C4×#48211yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—222no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23#6694612yes—
558C23C2×D4×D1111yescharacteristic
559D4—222no—
560D4—222no—
561D4—448no—
562D4—441no—
563D4—441no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—112no—
583C2×C4—112no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—444no—
598C2×C4—444no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—884no—
606C2×C4#6694612yes—
607C2×C4C22×C4×D1111yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4C2×#434311yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#41×D1111yescharacteristic
613C8—22no—
614C8—22no—
615C8—441no—
616C8—441no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22—881no—
628C22—881no—
629C22—881no—
630C22—881no—
631C22C2×#6694611yescharacteristic
632C22#1062311711yescharacteristic
633C22D11×#12311yescharacteristic
634C22D11×#13511yescharacteristic
635C22D11×#13511yescharacteristic
636C22D11×AGL(1,ℤ/8)11yescharacteristic
637C22#1062330811yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—114no—
644C4—222no—
645C4—222no—
646C4—442no—
647C4—442no—
648C4—442no—
649C4—441no—
650C4C4×#434111yescharacteristic
651C4C4×#434111yescharacteristic
652C4#1062315511yescharacteristic
653C4#1062315511yescharacteristic
654C2—42no—
655C2—882no—
656C2#1307113511yescharacteristic
657C2#1307738711yescharacteristic
658C2#1307742311yescharacteristic
659C2D11×#48211yescharacteristic
660C2#1307853411yescharacteristic
661C2#1307863511yescharacteristic
662C2#1307866911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1854D11
hypocenterC11C4×#482
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
3. #117×Dic11C2semidirect
4. #13069242C2semidirect
5. #13069235C2semidirect
6. #13069207C2semidirect
7. #13069200C2semidirect
9. #13068708C2semidirect
10. #107×Dic11C2semidirect
11. #106×Dic11C2semidirect
12. #13068430C2semidirect
13. #13068430C2semidirect
14. C22⋊C8×Dic11C2semidirect
15. C11×#1854C2semidirect
47. #10622350C4semidirect
85. #66979C2×C4semidirect
109. C11×C22⋊C8C2×C4semidirect
118. #66885C2×C4semidirect
119. #66885C2×C4semidirect
120. #66882C2×C4semidirect
121. #66881C2×C4semidirect
221. #1854D11semidirect
381. Dic11#482semidirect
438. C22⋊C8C4×D11semidirect
543. C11C4×#482semidirect

Maximal subgroups

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

subgroupindex
C2×#106223502
#130711222
#117×Dic112
#130692422
#130692352
#130692072
#130692002
#130689382
#130687082
#107×Dic112
#106×Dic112
#130684302
C22⋊C8×Dic112
C11×#18542
C4×#48211