Finite Group Databasebeta

← #14760296

Subgroups — #14760296

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×#10622654C211yesmaximal, characteristic
2C2×#10622371C211yesmaximal, characteristic, complemented
3C2×#10622735C211yesmaximal, characteristic, complemented
4#13071311C211yesmaximal, characteristic
5#13071294C211yesmaximal, characteristic, complemented
6#13069471C211yesmaximal, characteristic, complemented
7#13069343C211yesmaximal, characteristic, complemented
8#13069310C211yesmaximal, characteristic, complemented
9#13069307C211yesmaximal, characteristic, complemented
10#13069049C211yesmaximal, characteristic, complemented
11#13068639C211yesmaximal, characteristic, complemented
12#13068504C211yesmaximal, characteristic, complemented
13#13068445C211yesmaximal, characteristic, complemented
14#13068443C211yesmaximal, characteristic, complemented
15C11×#1895C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622834—21no—
28#10622834C2211yescharacteristic
29#10622833—21no—
30C2×#66896C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622735—24no—
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622654C418yescomplemented
40#10622598C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622587C2211yescharacteristic
44#10622586C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49#10622564—21no—
50#10622563—21no—
51#10622558—21no—
52#10622557—21no—
53#10622371—24no—
54#10622268—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C22×Dic22C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#121—22no—
73C11×#121C2×C414yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86D4×Dic11—22no—
87D4×Dic11—22no—
88C2×#4324—22no—
89C2×#4324—22no—
90C2×#4324C2×C414yes—
91#66979—22no—
92#66979—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977C2×C414yescomplemented
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8—22no—
110C22×C11⋊C8—22no—
111C22×C11⋊C8C2×C414yescomplemented
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114#66940—22no—
115#66940—22no—
116C11×#102—22no—
117C11×#102—22no—
118C11×#95—21no—
119#66896C2×C414yes—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66880—22no—
128#66880—22no—
129#66879—22no—
130#66879—22no—
131C8×Dic11—22no—
132C8×Dic11D414yescomplemented
133#66874C2×C414yescomplemented
134#66872—22no—
135#66872—22no—
136#66872C2×C414yescomplemented
137#21523—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—81no—
147C2×D4×C11—81no—
148C2×D4×C11C22×C412yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—81no—
166C22×Dic11—81no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
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×C11—21no—
181C2×C8×C11—21no—
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⋊C4C22×C412yes—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—81no—
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194C22⋊Dic11—24no—
195C22⋊Dic11—42no—
196C22⋊Dic11—81no—
197C22⋊Dic11—81no—
198C22⋊Dic11—81no—
199#4324—28no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—81no—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—42no—
211Dic11⋊C4—81no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C4×Dic11—81no—
216C4×Dic11—81no—
217C4×Dic11C2×D412yes—
218C4×Dic11#4112yes—
219C2×C11⋊C8—28no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C22×C412yes—
223C2×C11⋊C8C22×C412yes—
224C2×C11⋊C8C2×D412yes—
225C2×C11⋊C8#4112yes—
226C2×#465—111no—
227C2×C4×SD16—111no—
228C2×#405—111no—
229#2324—111no—
230#2323—111no—
231#1968—111no—
232#1941—111no—
233#1936—111no—
234#1935—111no—
235#1895D1111yescharacteristic
236#1894—111no—
237#1807—111no—
238C4×#106—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×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11C4×D412yes—
255C23×C11C22×D411yescharacteristic
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—84no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
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—41no—
275C2×C4×C11—41no—
276C2×C4×C11C4×D412yes—
277C2×C4×C11C23×C411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
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—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—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—84no—
306C2×Dic11#12112yes—
307C2×Dic11#12112yes—
308Dic22—22no—
309Dic22—22no—
310Dic22—41no—
311Dic22—41no—
312C8×C11—22no—
313C8×C11—22no—
314C11⋊C8—22no—
315C11⋊C8C4×D414yes—
316C22×SD16—111no—
317C22×M16C2×D1111yescharacteristic
318C23×C8—111no—
319C2×C22⋊Q8—111no—
320C2×#121C2×D1111yescharacteristic
321C2×C4×Q8—111no—
322C2×C4×D4—111no—
323C2×#117—111no—
324#465—118no—
325C4×SD16—224no—
326C2×#106—111no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#102—111no—
333C2×#102C2×D1111yescharacteristic
334C2×#102C2×D1111yescharacteristic
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#380—111no—
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×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11C2×C4×D411yescharacteristic
377C22×C11C2×#12111yescharacteristic
378C22×C11#53211yescharacteristic
379C22×C11#57711yescharacteristic
380C22×C11#57711yescharacteristic
381C22×C11#57711yescharacteristic
382C22×C11#57711yescharacteristic
383C4×C11—22no—
384C4×C11—42no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11C2×C4×D411yescharacteristic
388C4×C11C4×#4111yescharacteristic
389C4×C11#52511yescharacteristic
390C4×C11#52911yescharacteristic
391Dic11—22no—
392Dic11—22no—
393Dic11—42no—
394Dic11—41no—
395Dic11—41no—
396Dic11—42no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8—111no—
400C22×D4—21no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—221no—
403C23×C4C22×D1111yescharacteristic
404C2×SD16—114no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C22×C8—111no—
411C22×C8—114no—
412C22×C8—111no—
413C22×C8—222no—
414C22×C8—222no—
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C22⋊Q8—114no—
418C22⋊Q8—222no—
419#121—22no—
420#121C4×D1114yes—
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—111no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
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#106—114no—
454#106—222no—
455#106—222no—
456#103—114no—
457#103—222no—
458#103—222no—
459#102—22no—
460#102—22no—
461#102—114no—
462#97—222no—
463#97—222no—
464C4×C8—114no—
465C4×C8—222no—
466#95—21no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474C2×C11—42no—
475C2×C11—82no—
476C2×C11C4×#12111yescharacteristic
477C2×C11#294911yescharacteristic
478C2×C11#295211yescharacteristic
479C2×C11#305711yescharacteristic
480C2×C11#306011yescharacteristic
481C2×C11#317311yescharacteristic
482C2×C11#317411yescharacteristic
483C24—21no—
484C24D4×D1111yescharacteristic
485C2×Q8—112no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C2×C4×D1112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—221no—
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#434112yes—
521C22×C4C23×D1111yescharacteristic
522SD16—228no—
523M16—28no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—112no—
529C2×C8—112no—
530C2×C8—112no—
531C2×C8—112no—
532C2×C8—228no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8D4×D1112yes—
536C2×C8#434112yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—112no—
543C4⋊C4—222no—
544C4⋊C4—222no—
545C4⋊C4—224no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—442no—
552C4⋊C4—881no—
553C4⋊C4—881no—
554C4⋊C4C2×C4×D1112yes—
555C22⋊C4—24no—
556C22⋊C4—81no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—224no—
560C22⋊C4—442no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C22⋊C4—881no—
564C42—112no—
565C42—112no—
566C42—221no—
567C42—221no—
568C42—442no—
569C42—881no—
570C42—881no—
571C11#2152311yescharacteristic, complemented, Sylow
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23(C22⋊D11)⋊C412yes—
586C23C2×D4×D1111yescharacteristic
587Q8—222no—
588Q8—222no—
589Q8—441no—
590Q8—441no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—84no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
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—112no—
612C2×C4—112no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—884no—
636C2×C4(C22⋊D11)⋊C412yes—
637C2×C4C22×C4×D1111yescharacteristic
638C2×C4C2×D4×D1111yescharacteristic
639C2×C4C2×#434111yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C8—22no—
644C8—22no—
645C8—114no—
646C8—222no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×(C22⋊D11)⋊C411yescharacteristic
662C22#1062312711yescharacteristic
663C22D11×#12111yescharacteristic
664C22#1062330611yescharacteristic
665C22#1062330611yescharacteristic
666C22#1062330611yescharacteristic
667C22#1062330911yescharacteristic
668C4—22no—
669C4—42no—
670C4—81no—
671C4—81no—
672C4—222no—
673C4—222no—
674C4—441no—
675C4—442no—
676C4—441no—
677C4—442no—
678C4—881no—
679C4—881no—
680C4C4×#434111yescharacteristic
681C4C4×D4×D1111yescharacteristic
682C4#1062311711yescharacteristic
683C4#1062318011yescharacteristic
684C2—42no—
685C2—82no—
686C2#1307112611yescharacteristic
687C2#1307747811yescharacteristic
688C2#1307749511yescharacteristic
689C2#1307825311yescharacteristic
690C2#1307827611yescharacteristic
691C2#1307922811yescharacteristic
692C2#1307923911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenter#1895D11
hypocenterC11#21523
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#10622371C2semidirect
3. C2×#10622735C2semidirect
5. #13071294C2semidirect
6. #13069471C2semidirect
7. #13069343C2semidirect
8. #13069310C2semidirect
9. #13069307C2semidirect
10. #13069049C2semidirect
11. #13068639C2semidirect
12. #13068504C2semidirect
13. #13068445C2semidirect
14. #13068443C2semidirect
39. #10622654C4semidirect
100. #66977C2×C4semidirect
111. C22×C11⋊C8C2×C4semidirect
132. C8×Dic11D4semidirect
133. #66874C2×C4semidirect
136. #66872C2×C4semidirect
571. C11#21523semidirect

Maximal subgroups

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

subgroupindex
C2×#106226542
C2×#106223712
C2×#106227352
#130713112
#130712942
#130694712
#130693432
#130693102
#130693072
#130690492
#130686392
#130685042
#130684452
#130684432
C11×#18952
#2152311