Finite Group Databasebeta

← #14767590

Subgroups — #14767590

Order 2816.

906 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
1C2×#10622780C211yesmaximal, characteristic
2C4×#66997C211yesmaximal, characteristic, complemented
3#13071163C211yesmaximal, characteristic
4#13069434C211yesmaximal, characteristic, complemented
5#13069431C211yesmaximal, characteristic
6#13068974C211yesmaximal, characteristic
7#13068958C211yesmaximal, characteristic, complemented
8#13068957C211yesmaximal, characteristic, complemented
9#13068956C211yesmaximal, characteristic, complemented
10#13068954C211yesmaximal, characteristic, complemented
11#13068952C211yesmaximal, characteristic
12#13068948C211yesmaximal, characteristic
13#13068748C211yesmaximal, characteristic, complemented
14#13068363C211yesmaximal, characteristic, complemented
15C11×#1880C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66989C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×Dic44C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C11×#390C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622780C418yescomplemented
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37#10622590C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622587C2211yescharacteristic
40#10622585—21no—
41#10622585—21no—
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44#10622557—21no—
45#10622557—21no—
46C22⋊C4×Dic11—21no—
47C22⋊C4×Dic11—21no—
48C4×Dic11⋊C4—21no—
49C4×Dic11⋊C4—21no—
50C42×Dic11C2211yescharacteristic
51#10622542C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C2×C11×SD16C2×C414yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—41no—
71C4×Q8×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#66997—22no—
83#66997C2×C414yescomplemented
84C2×#4326—41no—
85C2×#4326—41no—
86C2×#4326C2×C414yescomplemented
87#66989—22no—
88#66989C2×C414yes—
89D4×Dic11—41no—
90D4×Dic11—41no—
91C2×#4324—41no—
92C2×#4324—41no—
93C2×#4324C2×C414yes—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×Dic44—41no—
113C2×Dic44—41no—
114C2×Dic44C2×C414yescomplemented
115#66940—41no—
116#66940—41no—
117C4×Dic22—41no—
118C4×Dic22—41no—
119C11×#103—41no—
120C11×#102—41no—
121#66899—41no—
122#66896—41no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131#66880—41no—
132#66880—41no—
133#66879—22no—
134#66879C2×C414yescomplemented
135#66874—41no—
136#66874—41no—
137#22273—111nomaximal, Sylow
138C24×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22C22×C412yes—
179C2×Dic22C22×C412yes—
180C11×SD16—44no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C22×C412yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—42no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—42no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—42no—
197C22⋊Dic11—24no—
198C22⋊Dic11—24no—
199C22⋊Dic11—42no—
200#4326—44no—
201#4324—44no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212C4×Dic11—22no—
213C4×Dic11—22no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—41no—
217C4×Dic11—41no—
218C4×Dic11—42no—
219C4×Dic11—42no—
220C4×Dic11C22×C412yes—
221C4×Dic11#4112yes—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8C22×C412yes—
228Dic44—44no—
229C2×#497—111no—
230C4×C4⋊Q8—111no—
231C4×#124—111no—
232#1960—111no—
233#1959—111no—
234#1880—111no—
235#1880D1111yescharacteristic
236#1878—111no—
237#1878—111no—
238#1878—111no—
239#1878—111no—
240#1877—111no—
241#1877—111no—
242#1836—111no—
243#1745—111no—
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11C22×D411yescharacteristic
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—41no—
255Q8×C11—41no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—41no—
259D4×C11—41no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
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—41no—
273C2×C4×C11—41no—
274C2×C4×C11#13712yes—
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—84no—
303C2×Dic11C4×D412yes—
304C2×Dic11C4×D412yes—
305C2×Dic11#13712yes—
306Dic22—22no—
307Dic22—22no—
308Dic22—22no—
309Dic22—22no—
310Dic22—41no—
311Dic22—41no—
312Dic22—41no—
313Dic22—41no—
314C8×C11—22no—
315C8×C11—41no—
316C11⋊C8—22no—
317C11⋊C8—41no—
318C22×Q16—111no—
319C22×Q16—111no—
320C22×SD16—111no—
321C22×SD16C2×D1111yescharacteristic
322C2×C4⋊Q8—111no—
323C2×#124—111no—
324C2×C4×Q8—111no—
325C2×C4×Q8—111no—
326C2×C4×Q8C2×D1111yescharacteristic
327C2×C4×D4—111no—
328#497—118no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103C2×D1111yescharacteristic
335C2×#102—111no—
336C2×#102C2×D1111yescharacteristic
337C2×#97—111no—
338C2×#97—111no—
339#391—111no—
340#391—111no—
341#391—111no—
342#390C2×D1111yescharacteristic
343#389—221no—
344#389—221no—
345#388—221no—
346#388—221no—
347#384—111no—
348#382—111no—
349C4×C4⋊C4—221no—
350C4×C4⋊C4—221no—
351C4×C22⋊C4—221no—
352C4×C22⋊C4—221no—
353C43—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340C2×D1111yescharacteristic
358#336—111no—
359#336—111no—
360#336—111no—
361#336C2×D1111yescharacteristic
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11C2×C4×D411yescharacteristic
370C22×C11#53511yescharacteristic
371C22×C11#53511yescharacteristic
372C22×C11C2×#13711yescharacteristic
373C22×C11C2×#13711yescharacteristic
374C22×C11#57511yescharacteristic
375C22×C11#57511yescharacteristic
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—41no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11#51811yescharacteristic
382C4×C11#51811yescharacteristic
383C4×C11#54011yescharacteristic
384C4×C11#54011yescharacteristic
385Dic11—22no—
386Dic11—22no—
387Dic11—22no—
388Dic11—42no—
389Dic11—42no—
390Dic11—41no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8—111no—
394C22×Q8—111no—
395C22×Q8C22×D1111yescharacteristic
396C22×D4C22×D1111yescharacteristic
397C23×C4—221no—
398C2×Q16—114no—
399C2×Q16—114no—
400C2×Q16—441no—
401C2×Q16—441no—
402C2×Q16—441no—
403C2×Q16—441no—
404C2×SD16—41no—
405C2×SD16—41no—
406C2×SD16—114no—
407C2×SD16—441no—
408C2×SD16—441no—
409C2×SD16C4×D1114yes—
410C22×C8—111no—
411C22×C8—111no—
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414C4⋊Q8—114no—
415C4⋊Q8—222no—
416#124—114no—
417#124—222no—
418C4×Q8—41no—
419C4×Q8—41no—
420C4×Q8—441no—
421C4×Q8—441no—
422C4×Q8—441no—
423C4×Q8—441no—
424C4×D4—441no—
425C4×D4—441no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C42—21no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452#103—41no—
453#103—441no—
454#103—441no—
455#103—441no—
456#103—441no—
457#103—441no—
458#102—41no—
459#102—441no—
460#97—114no—
461#97—222no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11—82no—
471C2×C11#232811yescharacteristic
472C2×C11C4×#13711yescharacteristic
473C2×C11C4×#13711yescharacteristic
474C2×C11#321511yescharacteristic
475C2×C11#321611yescharacteristic
476C2×C11#321811yescharacteristic
477C2×C11#321911yescharacteristic
478C24—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—112no—
485C2×Q8—112no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8C2×C4×D1112yes—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4C2×C4×D1112yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4D4×D1111yescharacteristic
518C22×C4D4×D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520Q16—444no—
521Q16—444no—
522SD16—44no—
523SD16—444no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—112no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8C2×C4×D1112yes—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—42no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—224no—
554C22⋊C4—224no—
555C22⋊C4—442no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42—112no—
560C42—112no—
561C42—222no—
562C42—222no—
563C42—221no—
564C42—221no—
565C42—441no—
566C42—441no—
567C42—442no—
568C42—442no—
569C11#2227311yescharacteristic, complemented, Sylow
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C2×D4×D1111yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—41no—
581Q8—41no—
582Q8—222no—
583Q8—222no—
584Q8—222no—
585Q8—222no—
586Q8—441no—
587Q8—441no—
588Q8—441no—
589Q8—441no—
590D4—22no—
591D4—22no—
592D4—41no—
593D4—41no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—112no—
609C2×C4—112no—
610C2×C4—112no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—884no—
633C2×C4#6696812yes—
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704211yescharacteristic
640C8—22no—
641C8—41no—
642C8—222no—
643C8—441no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22C4×D4×D1111yescharacteristic
652C22#1062312311yescharacteristic
653C22#1062313811yescharacteristic
654C22C2×#6696811yescharacteristic
655C22#1062329911yescharacteristic
656C22#1062330411yescharacteristic
657C22D11×#13711yescharacteristic
658C4—22no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—222no—
664C4—222no—
665C4—222no—
666C4—441no—
667C4—442no—
668C4—442no—
669C4—881no—
670C4—881no—
671C4#1062301711yescharacteristic
672C4#1062307611yescharacteristic
673C4#1062314611yescharacteristic
674C4#1062319411yescharacteristic
675C2—82no—
676C2#1307133711yescharacteristic
677C2C4×#6696811yescharacteristic
678C2#1307743811yescharacteristic
679C2#1307961711yescharacteristic
680C2#1307962511yescharacteristic
681C2#1307964111yescharacteristic
682C2#1307965111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1880D11
hypocenterC11#22273
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C4×#66997C2semidirect
4. #13069434C2semidirect
7. #13068958C2semidirect
8. #13068957C2semidirect
9. #13068956C2semidirect
10. #13068954C2semidirect
13. #13068748C2semidirect
14. #13068363C2semidirect
32. #10622780C4semidirect
83. #66997C2×C4semidirect
86. C2×#4326C2×C4semidirect
114. C2×Dic44C2×C4semidirect
134. #66879C2×C4semidirect
569. C11#22273semidirect

Maximal subgroups

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

subgroupindex
C2×#106227802
C4×#669972
#130711632
#130694342
#130694312
#130689742
#130689582
#130689572
#130689562
#130689542
#130689522
#130689482
#130687482
#130683632
C11×#18802
#2227311