Finite Group Databasebeta

← #14797667

Subgroups — #14797667

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622852C211yesmaximal, characteristic
2C2×#10622371C211yesmaximal, characteristic, complemented
3#13072121C211yesmaximal, characteristic, complemented
4#13071446C211yesmaximal, characteristic
5#13070162C211yesmaximal, characteristic, complemented
6#13070053C211yesmaximal, characteristic, complemented
7#13069937C211yesmaximal, characteristic, complemented
8#13069820C211yesmaximal, characteristic, complemented
9#13069294C211yesmaximal, characteristic, complemented
10#13069225C211yesmaximal, characteristic, complemented
11#13068954C211yesmaximal, characteristic, complemented
12#13068948C211yesmaximal, characteristic, complemented
13#13068865C211yesmaximal, characteristic, complemented
14#13068624C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×#4326C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622852—24no—
30#10622843C2211yescharacteristic
31#10622843C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622833—21no—
34#10622833—21no—
35C2×#66896C2211yescharacteristic
36#10622825C2211yescharacteristic
37#10622824—21no—
38C4×C22⋊Dic11C2211yescharacteristic
39C2×C11⋊#95—21no—
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46#10622598C2211yescharacteristic
47#10622590C2211yescharacteristic
48#10622587C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50#10622565—21no—
51#10622564—21no—
52#10622371—24no—
53#10622271—21no—
54#10622267—21no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C23×Dic11—21no—
73C23×Dic11—21no—
74C22×Dic22C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86C2×#4326—22no—
87C2×#4326—22no—
88C2×#4326—41no—
89D4×Dic11—22no—
90D4×Dic11—22no—
91D4×Dic11—41no—
92D4×Dic11—41no—
93C2×#4324—22no—
94C2×#4324—22no—
95C2×#4324D414yes—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100#66977—22no—
101#66977—41no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66940—22no—
110#66940—41no—
111C11×#103—22no—
112C11×#103—41no—
113C11×#102—22no—
114C11×#102—22no—
115C11×C22⋊C8—41no—
116C11×#95—21no—
117#66899—22no—
118#66896—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131C22⋊(C11⋊C8)—22no—
132#66882—41no—
133#66880—22no—
134#66880—41no—
135Dic11⋊C8—41no—
136C8×Dic11—22no—
137#66872—22no—
138#24903—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11#4112yes—
151C2×D4×C11—24no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11C2×D412yes—
158C2×D4×C11#4112yes—
159C2×D4×C11#4112yes—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—42no—
179C22×Dic11—42no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11—81no—
183C22×Dic11—81no—
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22C2×D412yes—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C22⋊C4—42no—
205C22⋊Dic11—22no—
206C22⋊Dic11—41no—
207C22⋊Dic11—42no—
208C22⋊Dic11—42no—
209C22⋊Dic11—42no—
210C22⋊Dic11—81no—
211#4326—44no—
212#4324—28no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—42no—
220Dic11⋊C4—42no—
221Dic11⋊C4—42no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—42no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8C2×D412yes—
233C2×#452—111no—
234C2×C4×SD16—111no—
235#2421—111no—
236#2339—111no—
237#2097—111no—
238#2077—111no—
239#2056—111no—
240#2036—111no—
241#1933—111no—
242#1923—111no—
243#1878—111no—
244#1877—111no—
245#1862—111no—
246#1804—111no—
247#1788D1111yescharacteristic
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11C22×D411yescharacteristic
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—41no—
266Q8×C11—41no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—48no—
271D4×C11#12314yes—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—48no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—22no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—84no—
319C2×Dic11—84no—
320C2×Dic11#13512yes—
321Dic22—22no—
322Dic22—22no—
323Dic22—41no—
324Dic22—41no—
325C8×C11—41no—
326C8×C11—41no—
327C11⋊C8—22no—
328C11⋊C8—41no—
329C22×#41C2×D1111yescharacteristic
330C22×Q16—111no—
331C22×SD16—111no—
332C2×C22⋊Q8—111no—
333C2×C4×Q8—111no—
334C2×C4×D4—111no—
335C2×C4×D4—111no—
336#452—224no—
337C4×SD16—224no—
338C2×#107—111no—
339C2×#106—111no—
340C2×C4⋊C8—111no—
341C2×#103—111no—
342C2×#103—111no—
343C2×#103—111no—
344C2×#103C2×D1111yescharacteristic
345C2×#103C2×D1111yescharacteristic
346C2×#102—111no—
347C2×#102C2×D1111yescharacteristic
348C2×#102C2×D1111yescharacteristic
349C2×C22⋊C8—111no—
350C2×C22⋊C8C2×D1111yescharacteristic
351C2×C4×C8—111no—
352#400—221no—
353#397—221no—
354#391—111no—
355#391—111no—
356#391—111no—
357#389—111no—
358#388—221no—
359#387—221no—
360#386—221no—
361#386—221no—
362#382—111no—
363#381—221no—
364#380—111no—
365#380C2×D1111yescharacteristic
366C4×C22⋊C4—111no—
367C2×#95—221no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#336—111no—
373#336—111no—
374C22×C11—24no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11#52511yescharacteristic
389C22×C11D4211yescharacteristic
390C22×C11#54611yescharacteristic
391C22×C11C2×#13511yescharacteristic
392C22×C11#57511yescharacteristic
393C22×C11#57711yescharacteristic
394C22×C11#57811yescharacteristic
395C4×C11—41no—
396C4×C11—42no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11C2×#12311yescharacteristic
400C4×C11#53811yescharacteristic
401C4×C11#54611yescharacteristic
402C4×C11#55111yescharacteristic
403Dic11—22no—
404Dic11—42no—
405Dic11—41no—
406Dic11—41no—
407Dic11—41no—
408Dic11—81no—
409Dic11—81no—
410Dic11—81no—
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—41no—
416C2×#41—41no—
417C22×Q8—111no—
418C22×Q8C22×D1111yescharacteristic
419C22×D4—21no—
420C22×D4C22×D1111yescharacteristic
421C23×C4—21no—
422C23×C4—221no—
423C23×C4—221no—
424C23×C4C22×D1111yescharacteristic
425C2×Q16—222no—
426C2×Q16—222no—
427C2×Q16—441no—
428C2×SD16—114no—
429C2×SD16—222no—
430C2×SD16—222no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8C22×D1111yescharacteristic
434C22×C8C22×D1111yescharacteristic
435C22⋊Q8—222no—
436C22⋊Q8—441no—
437C4×Q8—222no—
438C4×Q8—441no—
439C4×D4—222no—
440C4×D4—222no—
441C4×D4—441no—
442C4×D4—441no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4—221no—
449C2×C4⋊C4C22×D1111yescharacteristic
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—111no—
453C2×C22⋊C4—111no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C42—111no—
459C2×C42—111no—
460C2×C42—221no—
461#107—441no—
462#106—222no—
463C4⋊C8—441no—
464#103—22no—
465#103—41no—
466#103—222no—
467#103—222no—
468#103—441no—
469#102—22no—
470#102—22no—
471#102—222no—
472C22⋊C8—41no—
473C22⋊C8—222no—
474C4×C8—222no—
475#95—21no—
476#95—111no—
477#95—111no—
478#95—221no—
479#95—221no—
480#95—221no—
481#95—221no—
482#95—221no—
483#95—221no—
484#95—221no—
485#95—221no—
486#95—221no—
487#95—221no—
488C2×C11—44no—
489C2×C11—81no—
490C2×C11#241811yescharacteristic
491C2×C11#310211yescharacteristic
492C2×C11#312011yescharacteristic
493C2×C11#326911yescharacteristic
494C2×C11#328211yescharacteristic
495C2×C11#330211yescharacteristic
496C2×C11#332311yescharacteristic
497C24—21no—
498C24D4×D1111yescharacteristic
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—112no—
509C2×Q8—221no—
510C2×Q8—221no—
511C2×Q8—221no—
512C2×Q8—221no—
513C2×Q8—221no—
514C2×Q8#434112yes—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4#433912yes—
522C2×D4D4×D1112yes—
523C2×D4#434112yes—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—111no—
537C22×C4—111no—
538C22×C4—111no—
539C22×C4—111no—
540C22×C4—221no—
541C22×C4—221no—
542C22×C4—221no—
543C22×C4—221no—
544C22×C4—442no—
545C22×C4—442no—
546C22×C4—442no—
547C22×C4—442no—
548C22×C4—881no—
549C22×C4—881no—
550C22×C4D4×D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552Q16—444no—
553SD16—228no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—112no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—221no—
571C4⋊C4—221no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—442no—
577C4⋊C4—442no—
578C4⋊C4—442no—
579C22⋊C4—42no—
580C22⋊C4—222no—
581C22⋊C4—441no—
582C22⋊C4—442no—
583C22⋊C4—442no—
584C22⋊C4—442no—
585C22⋊C4—881no—
586C42—221no—
587C42—221no—
588C42—221no—
589C42—221no—
590C42—442no—
591C11#2490311yescharacteristic, complemented, Sylow
592C23—22no—
593C23—22no—
594C23—22no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C2×D4×D1111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—222no—
612Q8—222no—
613Q8—441no—
614Q8—441no—
615D4—22no—
616D4—22no—
617D4—22no—
618D4—48no—
619D4#6693614yes—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—48no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—112no—
638C2×C4—221no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—221no—
643C2×C4—221no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—221no—
647C2×C4—221no—
648C2×C4—221no—
649C2×C4—222no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—884no—
662C2×C4—884no—
663C2×C4C2×#433911yescharacteristic
664C2×C4C2×D4×D1111yescharacteristic
665C2×C4C2×#434111yescharacteristic
666C2×C4C2×#434111yescharacteristic
667C2×C4#6703711yescharacteristic
668C2×C4#6703711yescharacteristic
669C8—41no—
670C8—41no—
671C8—222no—
672C8—441no—
673C22—24no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22#1062302111yescharacteristic
688C22#1062311711yescharacteristic
689C22#1062312111yescharacteristic
690C22D11×#13511yescharacteristic
691C22#1062330211yescharacteristic
692C22#1062330411yescharacteristic
693C22#1062330911yescharacteristic
694C4—41no—
695C4—42no—
696C4—81no—
697C4—81no—
698C4—222no—
699C4—441no—
700C4—441no—
701C4—441no—
702C4—442no—
703C4—881no—
704C4—881no—
705C4—881no—
706C4C2×#6693611yescharacteristic
707C4#1062302611yescharacteristic
708C4#1062312211yescharacteristic
709C4#1062312411yescharacteristic
710C2—44no—
711C2—81no—
712C2#1307208211yescharacteristic
713C2#1307862711yescharacteristic
714C2#1307883111yescharacteristic
715C2#1308016911yescharacteristic
716C2#1308032111yescharacteristic
717C2#1308052911yescharacteristic
718C2#1308083311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenter#1788D11
hypocenterC11#24903
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622371C2semidirect
3. #13072121C2semidirect
5. #13070162C2semidirect
6. #13070053C2semidirect
7. #13069937C2semidirect
8. #13069820C2semidirect
9. #13069294C2semidirect
10. #13069225C2semidirect
11. #13068954C2semidirect
12. #13068948C2semidirect
13. #13068865C2semidirect
14. #13068624C2semidirect
591. C11#24903semidirect

Maximal subgroups

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

subgroupindex
C2×#106228522
C2×#106223712
#130721212
#130714462
#130701622
#130700532
#130699372
#130698202
#130692942
#130692252
#130689542
#130689482
#130688652
#130686242
C11×#17882
#2490311