Finite Group Databasebeta

← #14760432

Subgroups — #14760432

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622747C211yesmaximal, characteristic
2C2×#10622465C211yesmaximal, characteristic, complemented
3C2×#10622735C211yesmaximal, characteristic, complemented
4#13071305C211yesmaximal, characteristic
5#13071294C211yesmaximal, characteristic, complemented
6#13069495C211yesmaximal, characteristic, complemented
7#13069352C211yesmaximal, characteristic, complemented
8#13069297C211yesmaximal, characteristic, complemented
9#13069290C211yesmaximal, characteristic, complemented
10#13069042C211yesmaximal, characteristic
11#13069037C211yesmaximal, characteristic, complemented
12#107×Dic11C211yesmaximal, characteristic, complemented
13#13068445C211yesmaximal, characteristic, complemented
14#13068440C211yesmaximal, characteristic, complemented
15C11×#1809C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622747C418yescomplemented
29#10622735—24no—
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622601C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47#10622570—21no—
48#10622569—21no—
49#10622558—21no—
50#10622557—21no—
51#10622465—24no—
52#10622283—21no—
53#10622281—21no—
54#10622268—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16C2×C414yescomplemented
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80C2×C22⋊Dic11D411yescharacteristic
81#66983—22no—
82#66983C2×C414yes—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87#66979—22no—
88#66979—22no—
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93#66977—22no—
94#66977C2×C414yescomplemented
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8—22no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×#4314—22no—
110C2×#4314—22no—
111C2×#4314C2×C414yes—
112#66946—22no—
113#66946—22no—
114#66940—22no—
115#66940—22no—
116C11×#107—22no—
117C11×#106—22no—
118C11×#95—21no—
119C11×#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126#66885C2×C414yes—
127#66882C2×C414yescomplemented
128#66880C2×C414yescomplemented
129#66879—22no—
130#66879—22no—
131C8×Dic11—22no—
132C8×Dic11D414yescomplemented
133#66874—22no—
134#66874—22no—
135#66873—22no—
136#66873—22no—
137#21535—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—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—21no—
147C22×C4×C11—21no—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—24no—
153C2×C22⋊D11—81no—
154C2×C22⋊D11—81no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44C22×C412yes—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22C22×C412yes—
177C11×M16—28no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C412yes—
181C2×C8×C11C22×C412yes—
182C2×C8×C11C2×D412yes—
183C2×C8×C11#4112yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C22⋊C4—81no—
193C11×C22⋊C4—81no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—81no—
200(C2×D11)⋊C4—81no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C22×C412yes—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—24no—
208Dic11⋊C4—42no—
209Dic11⋊C4—81no—
210Dic11⋊C4—81no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—42no—
214C4×Dic11—81no—
215C4×Dic11—81no—
216C4×Dic11C2×D412yes—
217C4×Dic11#4112yes—
218C2×C11⋊C8—28no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8C2×D412yes—
224C2×C11⋊C8#4112yes—
225#4314—28no—
226C2×#468—111no—
227C2×C4×SD16—111no—
228C2×#405—111no—
229#2324—111no—
230#2323—111no—
231#1973—111no—
232#1943—111no—
233#1934—111no—
234#1933—111no—
235#1893—111no—
236#1892—111no—
237#1809D1111yescharacteristic, complemented
238C4×#107—111no—
239#1763—111no—
240#1762—111no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11C4×D412yes—
248C23×C11C22×D411yescharacteristic
249C22×D11—22no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
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—41no—
273C2×C4×C11—41no—
274C2×C4×C11C4×D412yes—
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C22⋊D11—84no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11#12112yes—
302C2×Dic11#12112yes—
303D44—22no—
304D44—22no—
305D44—41no—
306D44—41no—
307C4×D11—84no—
308Dic22—22no—
309Dic22—22no—
310Dic22—41no—
311Dic22—41no—
312C8×C11—22no—
313C8×C11C4×D414yes—
314C11⋊C8—22no—
315C11⋊C8—22no—
316C22×SD16—111no—
317C22×M16C2×D1111yescharacteristic
318C23×C8—111no—
319C2×C22⋊Q8—111no—
320C2×#121—111no—
321C2×C4×Q8—111no—
322C2×C4×D4—111no—
323C2×#117—111no—
324#468—118no—
325C4×SD16—224no—
326C2×#107—111no—
327C2×#107C2×D1111yescharacteristic
328C2×#106C2×D1111yescharacteristic
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335#405—224no—
336C2×#97—111no—
337C2×#97—111no—
338C2×C4×C8—111no—
339C2×C4×C8—111no—
340#391—111no—
341#390—111no—
342#390—221no—
343#389—111no—
344#389—111no—
345#389—221no—
346#388—221no—
347#388—221no—
348#388—221no—
349#387—221no—
350#386—221no—
351#385—221no—
352#380C2×D1111yescharacteristic
353#380C2×D1111yescharacteristic
354C4×C4⋊C4—111no—
355C4×C4⋊C4—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340C2×D1111yescharacteristic
361#340C2×D1111yescharacteristic
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11C2×C4×D411yescharacteristic
370C22×C11C2×#12111yescharacteristic
371C22×C11#53211yescharacteristic
372C22×C11#57611yescharacteristic
373C22×C11#57711yescharacteristic
374C22×C11#57711yescharacteristic
375C22×C11#57811yescharacteristic
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C4×C11—22no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11C2×C4×D411yescharacteristic
389C4×C11C4×#4111yescharacteristic
390C4×C11#52511yescharacteristic
391C4×C11#52911yescharacteristic
392Dic11—22no—
393Dic11—22no—
394Dic11—42no—
395Dic11—42no—
396Dic11—41no—
397Dic11—41no—
398Dic11—42no—
399C22×Q8—111no—
400C22×D4—111no—
401C22×D4—221no—
402C23×C4—221no—
403C23×C4C22×D1111yescharacteristic
404C2×SD16—114no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×M16—22no—
408C2×M16—22no—
409C2×M16C4×D1114yescomplemented
410C22×C8—111no—
411C22×C8—111no—
412C22×C8—222no—
413C22×C8—222no—
414C22×C8—222no—
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C22⋊Q8—114no—
418C22⋊Q8—222no—
419#121—114no—
420#121—222no—
421C4×Q8—222no—
422C4×Q8—222no—
423C4×D4—222no—
424C4×D4—222no—
425#117—222no—
426#117—222no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
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×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—111no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—221no—
451C2×C42—221no—
452C2×C42—221no—
453#107—22no—
454#107—114no—
455#106—22no—
456#103—114no—
457#103—222no—
458#103—222no—
459#102—114no—
460#102—222no—
461#102—222no—
462#97—222no—
463#97—222no—
464C4×C8—114no—
465C4×C8—222no—
466#95—21no—
467#95—21no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474C2×C11—42no—
475C2×C11C4×#12111yescharacteristic
476C2×C11#294611yescharacteristic
477C2×C11#294711yescharacteristic
478C2×C11#305711yescharacteristic
479C2×C11#306111yescharacteristic
480C2×C11#317811yescharacteristic
481C2×C11#317911yescharacteristic
482D11—82no—
483C24—221no—
484C24D4×D1111yescharacteristic
485C2×Q8—112no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×D4—112no—
492C2×D4—224no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—881no—
499C2×D4—881no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—442no—
516C22×C4—881no—
517C22×C4—881no—
518C22×C4C2×C4×D1112yes—
519C22×C4D4×D1111yescharacteristic
520C22×C4#434312yes—
521C22×C4C23×D1111yescharacteristic
522SD16—228no—
523M16—28no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—112no—
527C2×C8—112no—
528C2×C8—228no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8C2×C4×D1112yes—
534C2×C8C2×C4×D1112yes—
535C2×C8D4×D1112yes—
536C2×C8#434112yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—112no—
546C4⋊C4—112no—
547C4⋊C4—222no—
548C4⋊C4—222no—
549C4⋊C4—224no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—442no—
553C4⋊C4—881no—
554C4⋊C4—881no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—224no—
560C22⋊C4—224no—
561C22⋊C4—442no—
562C22⋊C4—881no—
563C22⋊C4—881no—
564C42—112no—
565C42—112no—
566C42—221no—
567C42—221no—
568C42—442no—
569C42—881no—
570C42—881no—
571C11#2153511yescharacteristic, complemented, Sylow
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—222no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23#6694612yes—
586C23C2×D4×D1111yescharacteristic
587Q8—222no—
588Q8—222no—
589Q8—441no—
590Q8—441no—
591D4—222no—
592D4—222no—
593D4—441no—
594D4—441no—
595D4—884no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—884no—
636C2×C4#6694612yes—
637C2×C4C22×C4×D1111yescharacteristic
638C2×C4C2×D4×D1111yescharacteristic
639C2×C4C2×#434111yescharacteristic
640C2×C4C2×#434311yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C8—22no—
644C8—222no—
645C8—222no—
646C8(C22⋊D11)⋊C414yes—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—442no—
655C22—442no—
656C22—442no—
657C22—881no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22C2×#6694611yescharacteristic
662C22#1062312711yescharacteristic
663C22D11×#12111yescharacteristic
664C22#1062330511yescharacteristic
665C22#1062330611yescharacteristic
666C22#1062330911yescharacteristic
667C22#1062331011yescharacteristic
668C4—22no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—222no—
674C4—222no—
675C4—441no—
676C4—442no—
677C4—442no—
678C4—442no—
679C4—441no—
680C4C2×(C22⋊D11)⋊C411yescharacteristic
681C4#1062305311yescharacteristic
682C4#1062315511yescharacteristic
683C4#1062315811yescharacteristic
684C2—42no—
685C2—882no—
686C2#1307112211yescharacteristic
687C2#1307744611yescharacteristic
688C2#1307745711yescharacteristic
689C2#1307825311yescharacteristic
690C2#1307828411yescharacteristic
691C2#1307928511yescharacteristic
692C2#1307930011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#21535
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#10622465C2semidirect
3. C2×#10622735C2semidirect
5. #13071294C2semidirect
6. #13069495C2semidirect
7. #13069352C2semidirect
8. #13069297C2semidirect
9. #13069290C2semidirect
11. #13069037C2semidirect
12. #107×Dic11C2semidirect
13. #13068445C2semidirect
14. #13068440C2semidirect
15. C11×#1809C2semidirect
28. #10622747C4semidirect
69. C2×C11×M16C2×C4semidirect
94. #66977C2×C4semidirect
127. #66882C2×C4semidirect
128. #66880C2×C4semidirect
132. C8×Dic11D4semidirect
237. #1809D11semidirect
409. C2×M16C4×D11semidirect
571. C11#21535semidirect

Maximal subgroups

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

subgroupindex
C2×#106227472
C2×#106224652
C2×#106227352
#130713052
#130712942
#130694952
#130693522
#130692972
#130692902
#130690422
#130690372
#107×Dic112
#130684452
#130684402
C11×#18092
#2153511