Finite Group Databasebeta

← #14762849

Subgroups — #14762849

Order 2816.

1466 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2C2×#10622739C211yesmaximal, characteristic
3#13070998C211yesmaximal, characteristic
4#13069050C211yesmaximal, characteristic, complemented
5#13069049C211yesmaximal, characteristic, complemented
6#13069047C211yesmaximal, characteristic, complemented
7#13068927C212yesmaximal, complemented
8#13068925C212yesmaximal, complemented
9#13068705C212yesmaximal, complemented
10#13068549C212yesmaximal, complemented
11C11×#1894C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19D11×C22⋊Q8—24no—
20D11×C22⋊Q8C418yescomplemented
21C2×#66950C2211yescharacteristic
22C2×#66949—21no—
23C2×#66945C2212yes—
24C2×C4⋊C4×D11—21no—
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×C22⋊C4×D11—21no—
27C2×#66931—21no—
28C2×C11×#103C2212yescomplemented
29C11×#380C2211yescharacteristic
30C2×#66899C2212yescomplemented
31#10622825C2211yescharacteristic
32#10622739—24no—
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35C2×#66880C2212yescomplemented
36#10622600C2212yes—
37C2×#66874C2212yescomplemented
38#10622568—21no—
39C22⋊C4×Dic11—21no—
40#10622279—21no—
41#10622277—21no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11D411yescharacteristic
50C2×Q8×D11—22no—
51C2×Q8×D11—42no—
52C2×Q8×D11—42no—
53C2×Q8×D11C2×C414yes—
54C22×C4×D11—21no—
55C22×C4×D11—21no—
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C22×C4×D11C2×C414yes—
59C22×C4×D11D411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D414yes—
62C22×C4×D11C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C2×C11×M16—22no—
67C2×C11×M16—42no—
68C22×C8×C11C2312yes—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66999—22no—
79#66999C2×C414yes—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2311yescharacteristic
87#66977—22no—
88#66977C2×C414yes—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—22no—
93C2×#4318—22no—
94C2×#4318—42no—
95C22×C11⋊C8C2312yes—
96#66950—22no—
97#66950C2×C414yes—
98#66949—28no—
99#66945—42no—
100#66945—42no—
101C4⋊C4×D11—28no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11C2×C414yes—
104C22⋊C4×D11—28no—
105#66931—28no—
106C11×#103—42no—
107C11×#95—21no—
108#66899—42no—
109C11⋊#95—21no—
110C11⋊#95—22no—
111(C2×D11)⋊C8—24no—
112(C2×D11)⋊C8—24no—
113#66880—42no—
114#66874—42no—
115#21768—111nomaximal, Sylow
116C24×C11C2×D411yescharacteristic
117C23×D11—24no—
118C23×D11—42no—
119C23×D11—41no—
120C23×D11—41no—
121C23×D11C22⋊C414yes—
122C23×D11C2×D411yescharacteristic
123C23×D11C2×D411yescharacteristic
124C2×Q8×C11—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11C22×C412yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—42no—
141C22×Dic11C22⋊C414yes—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144Q8×D11—48no—
145Q8×D11—44no—
146Q8×D11—44no—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—48no—
156C2×C4×D11—44no—
157C2×C4×D11—44no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—44no—
161C2×C4×D11C22⋊C414yes—
162C2×C4×D11C22⋊C414yes—
163C2×C4×D11C22×C412yes—
164C2×C4×D11C22×C412yes—
165C2×C4×D11C2×D412yes—
166C2×C4×D11C2×D412yes—
167C2×Dic22—24no—
168C2×Dic22—21no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—44no—
172C2×Dic22C22×C412yes—
173C11×M16—44no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4C22×C412yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—42no—
184C22⋊Dic11—24no—
185C22⋊Dic11—42no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—44no—
189(C2×D11)⋊C4—44no—
190C4⋊Dic11—24no—
191C4⋊Dic11—21no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11C22×C412yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198C4×Dic11—44no—
199#4318—44no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C22×C22⋊Q8—111no—
204C2×#407—111no—
205#2280—111no—
206#1894—111no—
207#1894—111no—
208#1894—111no—
209#1894D1111yescharacteristic, complemented
210#1873—112no—
211#1873—112no—
212#1824—112no—
213#1787—112no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11C2×C22⋊C412yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—28no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—48no—
231C22×D11—48no—
232C22×D11C2×C22⋊C412yes—
233C22×D11C2×C22⋊C412yes—
234C22×D11#13714yes—
235Q8×C11—24no—
236Q8×C11—41no—
237Q8×C11—41no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11H(5,𝔽2)12yes—
254C2×C4×C11H(5,𝔽2)12yes—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—44no—
260C2×Dic11—42no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11C2×C22⋊C412yes—
267C2×Dic11C2×C22⋊C412yes—
268C4×D11—24no—
269C4×D11—24no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—44no—
275C4×D11—44no—
276C4×D11—48no—
277C4×D11—48no—
278Dic22—24no—
279Dic22—48no—
280Dic22—41no—
281Dic22—41no—
282C8×C11—42no—
283C11⋊C8—42no—
284C23×Q8—111no—
285C24×C4—111no—
286C22×M16—111no—
287C22×M16C2×D1111yescharacteristic
288C2×C22⋊Q8—111no—
289C2×C22⋊Q8—111no—
290C2×C22⋊Q8—118no—
291C2×C22⋊Q8—111no—
292C2×C22⋊Q8—221no—
293C2×C22⋊Q8—221no—
294C2×C22⋊Q8—224no—
295C2×C22⋊Q8C2×D1111yescharacteristic
296C2×#117—112no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—221no—
299C22×C22⋊C4—221no—
300C2×#103—112no—
301C2×#103—112no—
302C2×#103—112no—
303C2×#103C2×D1112yescomplemented
304#407—224no—
305C2×C22⋊C8—112no—
306C2×C22⋊C8—112no—
307#381—221no—
308#380—111no—
309#380—112no—
310#380C2×D1111yescharacteristic
311#379—221no—
312C4×C22⋊C4—221no—
313C4×C22⋊C4—221no—
314#340—112no—
315#340—112no—
316#340—112no—
317#340C2×D1112yescomplemented
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11C22×C22⋊C411yescharacteristic
324C22×C11#53412yes—
325C22×C11C2×#13712yes—
326C22×C11#57511yescharacteristic
327C22×C11#57511yescharacteristic
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—416no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11#41914yes—
339C4×C11—22no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—82no—
343C4×C11#51812yes—
344C4×C11#53411yescharacteristic
345C4×C11#53411yescharacteristic
346Dic11—22no—
347Dic11—22no—
348Dic11—42no—
349Dic11—42no—
350Dic11—82no—
351C25—111no—
352C22×Q8—114no—
353C22×Q8—111no—
354C22×Q8—221no—
355C22×Q8—222no—
356C22×Q8—442no—
357C22×Q8—442no—
358C22×Q8C22×D1111yescharacteristic
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—111no—
362C23×C4—114no—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—114no—
366C23×C4—221no—
367C23×C4—221no—
368C23×C4—442no—
369C23×C4—442no—
370C23×C4C22×D1111yescharacteristic
371C2×M16—22no—
372C2×M16—42no—
373C2×M16—222no—
374C2×M16—442no—
375C22×C8—112no—
376C22×C8C22×D1112yes—
377C22⋊Q8—22no—
378C22⋊Q8—114no—
379C22⋊Q8—114no—
380C22⋊Q8—114no—
381C22⋊Q8—228no—
382C22⋊Q8—228no—
383C22⋊Q8—222no—
384C22⋊Q8—222no—
385C22⋊Q8—222no—
386C22⋊Q8C4×D1114yes—
387#117—442no—
388#117—442no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—114no—
392C2×C4⋊C4—112no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—228no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1112yes—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—222no—
408C2×C22⋊C4—222no—
409C2×C22⋊C4—221no—
410C2×C42—222no—
411#103—42no—
412#103—442no—
413#103—442no—
414#103—442no—
415C22⋊C8—224no—
416C22⋊C8—224no—
417#95—21no—
418#95—222no—
419#95—221no—
420C2×C11—42no—
421C2×C11#230811yescharacteristic
422C2×C11C2×#41911yescharacteristic
423C2×C11#289611yescharacteristic
424C2×C11#319612yes—
425C2×C11#319612yes—
426D11—24no—
427D11—42no—
428C24—111no—
429C24—111no—
430C24—114no—
431C24—224no—
432C24—442no—
433C24—441no—
434C24—441no—
435C24D4×D1111yescharacteristic
436C2×Q8—21no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—112no—
440C2×Q8—224no—
441C2×Q8—221no—
442C2×Q8—222no—
443C2×Q8—222no—
444C2×Q8—444no—
445C2×Q8—448no—
446C2×Q8—444no—
447C2×Q8—444no—
448C2×Q8C2×C4×D1112yes—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—114no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—114no—
462C22×C4—114no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—222no—
472C22×C4—448no—
473C22×C4—444no—
474C22×C4—444no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—444no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4C2×C4×D1112yes—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1112yes—
484C22×C4C23×D1111yescharacteristic
485M16—44no—
486M16—444no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—222no—
493C4⋊C4—24no—
494C4⋊C4—21no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—112no—
498C4⋊C4—224no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—224no—
502C4⋊C4—221no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4C2×C4×D1112yes—
506C22⋊C4—24no—
507C22⋊C4—42no—
508C22⋊C4—224no—
509C22⋊C4—224no—
510C22⋊C4—224no—
511C22⋊C4—444no—
512C22⋊C4—444no—
513C22⋊C4—442no—
514C42—444no—
515C11#2176811yescharacteristic, complemented, Sylow
516C23—21no—
517C23—22no—
518C23—21no—
519C23—22no—
520C23—112no—
521C23—114no—
522C23—112no—
523C23—228no—
524C23—221no—
525C23—221no—
526C23—222no—
527C23—221no—
528C23—222no—
529C23—221no—
530C23—222no—
531C23—444no—
532C23—444no—
533C23—448no—
534C23—448no—
535C23C22⋊C4×D1112yes—
536C23C2×D4×D1111yescharacteristic
537Q8—24no—
538Q8—41no—
539Q8—41no—
540Q8—224no—
541Q8—448no—
542Q8—441no—
543Q8—441no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—112no—
557C2×C4—112no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—444no—
569C2×C4—444no—
570C2×C4—448no—
571C2×C4—448no—
572C2×C4—444no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4C22⋊C4×D1112yes—
580C2×C4C22×C4×D1111yescharacteristic
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4#6703712yes—
583C2×C4#6704212yes—
584C8—42no—
585C8—442no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—42no—
590C22—42no—
591C22—114no—
592C22—222no—
593C22—222no—
594C22—224no—
595C22—224no—
596C22—222no—
597C22—222no—
598C22—222no—
599C22—4416no—
600C22—442no—
601C22—442no—
602C22C2×C22⋊C4×D1111yescharacteristic
603C22#1062313612yes—
604C22#1062330411yescharacteristic
605C22D11×#13712yes—
606C22#1062330811yescharacteristic
607C4—22no—
608C4—42no—
609C4—42no—
610C4—82no—
611C4—222no—
612C4—222no—
613C4—442no—
614C4—442no—
615C4—882no—
616C4#1062307612yes—
617C4#1062312011yescharacteristic
618C4#1062318411yescharacteristic
619C2—42no—
620C2—224no—
621C2—442no—
622C2#1307119011yescharacteristic
623C2D11×#41911yescharacteristic
624C2#1307713211yescharacteristic
625C2#1307944112yes—
626C2#1307944712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1894D11
hypocenterC11#21768
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #13069050C2semidirect
5. #13069049C2semidirect
6. #13069047C2semidirect
7. #13068927C2semidirect
8. #13068925C2semidirect
9. #13068705C2semidirect
10. #13068549C2semidirect
11. C11×#1894C2semidirect
20. D11×C22⋊Q8C4semidirect
28. C2×C11×#103C22semidirect
30. C2×#66899C22semidirect
35. C2×#66880C22semidirect
37. C2×#66874C22semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
209. #1894D11semidirect
303. C2×#103C2×D11semidirect
317. #340C2×D11semidirect
515. C11#21768semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
C2×#106227392
#130709982
#130690502
#130690492
#130690472
#130689272
#130689252
#130687052
#130685492
C11×#18942
#2176811