Finite Group Databasebeta

← #14662035

Subgroups — #14662035

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622590C211yesmaximal, characteristic
2C2×#10622189C211yesmaximal, characteristic
3C2×#10622167C211yesmaximal, characteristic
4C2×#10622167C211yesmaximal, characteristic
5C2×#10622188C211yesmaximal, characteristic
6#13066845C211yesmaximal, characteristic
7C2×C11×#340C211yesmaximal, characteristic
8C23×C8×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19#10622590—22no—
20#10622590—22no—
21C11×#340—22no—
22#10622189—22no—
23#10622188C414yescomplemented
24#10622167—22no—
25#10622167—22no—
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11—21no—
31C23×Dic11D411yescharacteristic
32C23×Dic11D411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11C2×C412yes—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C4⋊C4D412yes—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D412yes—
63C2×C4⋊Dic11Q812yes—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11C2×C412yes—
69C2×C4×Dic11Q812yes—
70C22×C11⋊C8—21no—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8C2×C412yes—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81#11268—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q811yescharacteristic
102C22×C4×C11C2×Q811yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—41no—
135C22×Dic11—41no—
136C22×Dic11—41no—
137C22×Dic11C4⋊C412yes—
138C22×Dic11C4⋊C412yes—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—41no—
143C2×C8×C11—41no—
144C2×C8×C11—41no—
145C2×C8×C11—41no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162C4×Dic11—22no—
163C4×Dic11—22no—
164C4×Dic11—22no—
165C4×Dic11—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—41no—
171C2×C11⋊C8—41no—
172C2×C11⋊C8—41no—
173C2×#382—111no—
174C2×#340—111no—
175C2×#340—111no—
176C2×#340—111no—
177C2×#340D1111yescharacteristic
178C2×#336—111no—
179C4⋊#95—111no—
180C23×C11C2×C4⋊C411yescharacteristic
181C23×C11#12011yescharacteristic
182C23×C11#12111yescharacteristic
183C23×C11C22⋊Q811yescharacteristic
184C23×C11#12311yescharacteristic
185C23×C11#12411yescharacteristic
186C23×C11#12411yescharacteristic
187C23×C11#13511yescharacteristic
188C23×C11#13511yescharacteristic
189C23×C11#13511yescharacteristic
190C23×C11#13511yescharacteristic
191C23×C11AGL(1,ℤ/8)11yescharacteristic
192C23×C11AGL(1,ℤ/8)11yescharacteristic
193C23×C11#13711yescharacteristic
194C23×C11#13711yescharacteristic
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—81no—
202C2×C4×C11—81no—
203C2×C4×C11—81no—
204C2×C4×C11—81no—
205C2×C4×C11—81no—
206C2×C4×C11—81no—
207C2×C4×C11—81no—
208C2×C4×C11—81no—
209C2×C4×C11#11711yescharacteristic
210C2×C4×C11#11711yescharacteristic
211C2×C4×C11C4×D411yescharacteristic
212C2×C4×C11C4×D411yescharacteristic
213C2×C4×C11C4×D411yescharacteristic
214C2×C4×C11C4×Q811yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11#12111yescharacteristic
217C2×C4×C11C22⋊Q811yescharacteristic
218C2×C4×C11C22⋊Q811yescharacteristic
219C2×C4×C11C22⋊Q811yescharacteristic
220C2×C4×C11C22⋊Q811yescharacteristic
221C2×C4×C11#12311yescharacteristic
222C2×C4×C11#12311yescharacteristic
223C2×C4×C11#12311yescharacteristic
224C2×C4×C11#12311yescharacteristic
225C2×C4×C11#12411yescharacteristic
226C2×C4×C11#12411yescharacteristic
227C2×C4×C11#12511yescharacteristic
228C2×C4×C11#12511yescharacteristic
229C2×C4×C11#12511yescharacteristic
230C2×C4×C11#12511yescharacteristic
231C2×C4×C11#12511yescharacteristic
232C2×C4×C11#12611yescharacteristic
233C2×C4×C11#12611yescharacteristic
234C2×C4×C11#12611yescharacteristic
235C2×C4×C11#12611yescharacteristic
236C2×C4×C11C4⋊Q811yescharacteristic
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—81no—
258C2×Dic11—81no—
259C2×Dic11—81no—
260C2×Dic11—81no—
261C2×Dic11—81no—
262C2×Dic11—81no—
263C2×Dic11—81no—
264C2×Dic11—81no—
265C8×C11—42no—
266C11⋊C8—42no—
267C23×C8—111no—
268C23×C8C2×D1111yescharacteristic
269C22×C4⋊C4—111no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C42—111no—
274#382—222no—
275#382—222no—
276C2×#95—221no—
277C2×#95—221no—
278C2×#95—221no—
279C2×#95—221no—
280#340—22no—
281#340—222no—
282#340—222no—
283#340—222no—
284#336—114no—
285C22×C11#38211yescharacteristic
286C22×C11#38511yescharacteristic
287C22×C11#38911yescharacteristic
288C22×C11#39311yescharacteristic
289C22×C11#39411yescharacteristic
290C22×C11#39711yescharacteristic
291C22×C11#40011yescharacteristic
292C22×C11#42711yescharacteristic
293C22×C11#42711yescharacteristic
294C22×C11#42811yescharacteristic
295C22×C11#42811yescharacteristic
296C22×C11#44911yescharacteristic
297C22×C11#44911yescharacteristic
298C22×C11#45211yescharacteristic
299C22×C11#45211yescharacteristic
300C22×C11#46311yescharacteristic
301C22×C11#46311yescharacteristic
302C22×C11#46411yescharacteristic
303C22×C11#46411yescharacteristic
304C22×C11#47811yescharacteristic
305C22×C11#47811yescharacteristic
306C22×C11#47911yescharacteristic
307C22×C11#47911yescharacteristic
308C22×C11#48211yescharacteristic
309C22×C11#48211yescharacteristic
310C22×C11#48511yescharacteristic
311C22×C11#48511yescharacteristic
312C22×C11#48811yescharacteristic
313C22×C11#48811yescharacteristic
314C22×C11#48811yescharacteristic
315C22×C11#48811yescharacteristic
316C22×C11#48911yescharacteristic
317C22×C11#48911yescharacteristic
318C22×C11#49011yescharacteristic
319C22×C11#49111yescharacteristic
320C4×C11—82no—
321C4×C11—82no—
322C4×C11#38711yescharacteristic
323C4×C11#38711yescharacteristic
324C4×C11#38811yescharacteristic
325C4×C11#38811yescharacteristic
326C4×C11#39811yescharacteristic
327C4×C11#39811yescharacteristic
328C4×C11#40011yescharacteristic
329C4×C11#40011yescharacteristic
330Dic11—42no—
331Dic11—42no—
332Dic11—82no—
333Dic11—82no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—221no—
339C23×C4—221no—
340C23×C4C22×D1111yescharacteristic
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—112no—
348C22×C8—221no—
349C22×C8—221no—
350C22×C8—221no—
351C22×C8—221no—
352C22×C8—221no—
353C22×C8—221no—
354C22×C8C4×D1112yes—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4D4412yes—
378C2×C4⋊C4C22⋊D1112yes—
379C2×C42—112no—
380C2×C42—112no—
381C2×C42—221no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42—221no—
385#95—224no—
386#95—224no—
387#95—442no—
388#95—442no—
389C2×C11#144211yescharacteristic
390C2×C11#183511yescharacteristic
391C2×C11#183611yescharacteristic
392C2×C11#185411yescharacteristic
393C2×C11#185411yescharacteristic
394C2×C11#194911yescharacteristic
395C2×C11#194911yescharacteristic
396C2×C11#202511yescharacteristic
397C2×C11#202611yescharacteristic
398C2×C11#204211yescharacteristic
399C2×C11#204211yescharacteristic
400C2×C11#207311yescharacteristic
401C2×C11#207411yescharacteristic
402C2×C11#210111yescharacteristic
403C2×C11#210111yescharacteristic
404C24D4×D1111yescharacteristic
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—441no—
436C22×C4—441no—
437C22×C4—441no—
438C22×C4—441no—
439C22×C4—441no—
440C22×C4—441no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×D4411yescharacteristic
449C22×C4#433911yescharacteristic
450C22×C4#433911yescharacteristic
451C22×C4#433911yescharacteristic
452C22×C4#433911yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4#434111yescharacteristic
455C22×C4#434111yescharacteristic
456C22×C4#434111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4Q8×D1111yescharacteristic
459C22×C4Q8×D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—441no—
472C2×C8—441no—
473C2×C8—441no—
474C2×C8—441no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—441no—
488C4⋊C4—441no—
489C4⋊C4—441no—
490C4⋊C4—441no—
491C42—222no—
492C42—222no—
493C42—222no—
494C42—222no—
495C11#1126811yescharacteristic, complemented, Sylow
496C23#6693511yescharacteristic
497C23#6693611yescharacteristic
498C23#6693811yescharacteristic
499C23#6693811yescharacteristic
500C23C4⋊C4×D1111yescharacteristic
501C23#6694911yescharacteristic
502C23#6696411yescharacteristic
503C23#6696511yescharacteristic
504C23#6696711yescharacteristic
505C23#6696811yescharacteristic
506C23#6696911yescharacteristic
507C23#6696911yescharacteristic
508C23#6697111yescharacteristic
509C23#6697211yescharacteristic
510C23#6699211yescharacteristic
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—81no—
520C2×C4—81no—
521C2×C4—81no—
522C2×C4—81no—
523C2×C4—81no—
524C2×C4—81no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—881no—
546C2×C4—881no—
547C2×C4—881no—
548C2×C4—881no—
549C2×C4—881no—
550C2×C4—881no—
551C2×C4—881no—
552C2×C4—881no—
553C2×C4#6692511yescharacteristic
554C2×C4C4×D4411yescharacteristic
555C2×C4#6692811yescharacteristic
556C2×C4#6692911yescharacteristic
557C2×C4#6693011yescharacteristic
558C2×C4#6693211yescharacteristic
559C2×C4#6693211yescharacteristic
560C2×C4#6693211yescharacteristic
561C2×C4(C22⋊D11)⋊C411yescharacteristic
562C2×C4#6693611yescharacteristic
563C2×C4#6693811yescharacteristic
564C2×C4#6693911yescharacteristic
565C2×C4#6694011yescharacteristic
566C2×C4#6694211yescharacteristic
567C2×C4#6694211yescharacteristic
568C2×C4#6694211yescharacteristic
569C2×C4#6694211yescharacteristic
570C2×C4#6694211yescharacteristic
571C2×C4#6694911yescharacteristic
572C2×C4#6694911yescharacteristic
573C2×C4#6695011yescharacteristic
574C2×C4#6695011yescharacteristic
575C2×C4C4×C22⋊D1111yescharacteristic
576C2×C4#6698211yescharacteristic
577C2×C4#6698311yescharacteristic
578C2×C4#6698811yescharacteristic
579C2×C4#6699111yescharacteristic
580C2×C4#6699711yescharacteristic
581C8—42no—
582C8—442no—
583C22#1062226311yescharacteristic
584C22#1062227111yescharacteristic
585C22#1062228111yescharacteristic
586C22#1062228611yescharacteristic
587C22#1062237711yescharacteristic
588C22#1062237811yescharacteristic
589C22#1062238111yescharacteristic
590C22#1062238111yescharacteristic
591C22#1062239211yescharacteristic
592C22#1062239411yescharacteristic
593C22#1062239611yescharacteristic
594C22#1062239711yescharacteristic
595C22#1062240811yescharacteristic
596C22#1062241011yescharacteristic
597C22#1062241311yescharacteristic
598C22#1062241311yescharacteristic
599C22#1062242311yescharacteristic
600C22#1062242411yescharacteristic
601C22#1062242711yescharacteristic
602C22#1062242811yescharacteristic
603C22#1062247011yescharacteristic
604C22#1062247311yescharacteristic
605C22#1062247411yescharacteristic
606C22#1062248411yescharacteristic
607C22#1062249011yescharacteristic
608C22#1062249311yescharacteristic
609C22#1062249411yescharacteristic
610C22#1062250411yescharacteristic
611C22#1062256511yescharacteristic
612C22#1062257411yescharacteristic
613C22#1062258511yescharacteristic
614C22#1062276611yescharacteristic
615C22#1062277811yescharacteristic
616C22#1062277911yescharacteristic
617C22#1062279811yescharacteristic
618C4—82no—
619C4—82no—
620C4—442no—
621C4—442no—
622C4—882no—
623C4—882no—
624C4#1062226511yescharacteristic
625C4#1062226611yescharacteristic
626C4#1062227111yescharacteristic
627C4#1062227211yescharacteristic
628C4#1062255311yescharacteristic
629C4#1062255711yescharacteristic
630C4#1062259311yescharacteristic
631C4#1062259611yescharacteristic
632C2#1306687111yescharacteristic
633C2#1306874511yescharacteristic
634C2#1306874811yescharacteristic
635C2#1306881611yescharacteristic
636C2#1306881811yescharacteristic
637C2#1306938111yescharacteristic
638C2#1306938511yescharacteristic
639C2#1306976111yescharacteristic
640C2#1306976611yescharacteristic
641C2#1306985411yescharacteristic
642C2#1306985611yescharacteristic
643C2#1307003211yescharacteristic
644C2#1307003711yescharacteristic
645C2#1307018611yescharacteristic
646C2#1307018811yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#340C2
socle, prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#340D11
hypocenterC11#11268
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
23. #10622188C4semidirect
495. C11#11268semidirect

Maximal subgroups

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

subgroupindex
C2×#106225902
C2×#106221892
C2×#106221672
C2×#106221882
#130668452
C2×C11×#3402
#1126811