Finite Group Databasebeta

← #14810898

Subgroups — #14810898

Order 2816.

990 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×#10622707C211yesmaximal, characteristic, complemented
2C2×D11×#103C211yesmaximal, characteristic
3#13072314C211yesmaximal, characteristic
4#13071450C211yesmaximal, characteristic
5#13070157C211yesmaximal, characteristic, complemented
6#13069997C211yesmaximal, characteristic, complemented
7#13069993C211yesmaximal, characteristic, complemented
8#13068887C211yesmaximal, characteristic, complemented
9#13068885C211yesmaximal, characteristic, complemented
10#13068810C211yesmaximal, characteristic
11#13068795C211yesmaximal, characteristic
12#13068640C211yesmaximal, characteristic
13#13068620C211yesmaximal, characteristic, complemented
14#13068549C211yesmaximal, characteristic
15C11×#2024C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×#66999—21no—
19C22×C8×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622842—21no—
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622707—24no—
36#10622602—21no—
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622597—21no—
41#10622589C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50D11×#103—24no—
51#10622280—21no—
52#10622279—21no—
53#10622259—21no—
54#10622259—21no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C2×Q8×D11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—22no—
66C2×Q8×D11—41no—
67C2×Q8×D11—41no—
68C2×Q8×D11Q814yescomplemented
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11C2311yescharacteristic
72C22×Dic22—21no—
73C22×Dic22C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8—41no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83#66999—44no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C2×C8×D11—22no—
104C2×C8×D11—22no—
105C2×C8×D11—41no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108#66940—22no—
109#66940—41no—
110C4×Dic22—22no—
111C4×Dic22—41no—
112C11×#103—22no—
113C11×#103—41no—
114C11×#95—21no—
115C11×#95—21no—
116#66899—22no—
117#66899—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126(C2×D11)⋊C8—22no—
127#66881—41no—
128#66880—22no—
129#66880—22no—
130Dic11⋊C8—41no—
131#66874—22no—
132#66874D414yes—
133#66872—22no—
134#66872—22no—
135#66872—41no—
136C4⋊(C11⋊C8)—22no—
137#25955—111nomaximal, Sylow
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—42no—
145C2×Q8×C11—42no—
146C2×Q8×C11—81no—
147C2×Q8×C11C2×Q812yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162Q8×D11—28no—
163Q8×D11—44no—
164Q8×D11—44no—
165Q8×D11—44no—
166C2×C4×D11—24no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—81no—
176C2×C4×D11C2×Q812yes—
177C2×C4×D11#4112yes—
178C2×Dic22—24no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—42no—
183C2×Dic22—42no—
184C2×Dic22C2×D412yes—
185C2×Dic22C2×Q812yes—
186C2×Dic22#4112yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4C2×D412yes—
200C42×C11—21no—
201C42×C11—21no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—42no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4SD1614yes—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217Dic11⋊C4—42no—
218Dic11⋊C4—81no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8C2×D412yes—
229C8×D11—44no—
230C2×#475—111no—
231C22×#103—111no—
232#2440—111no—
233Q8×C22⋊C4—111no—
234#2096—111no—
235#2066—111no—
236#2066—111no—
237#2024D1111yescharacteristic, complemented
238#1865—111no—
239#1865—111no—
240#1853—111no—
241#1850—111no—
242#1807—111no—
243#1803—111no—
244#1787—111no—
245C23×C11C22×D411yescharacteristic
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11C22⋊Q812yes—
251C22×D11C2×SD1612yes—
252C22×D11#13712yes—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—84no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
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×C11—41no—
275C2×C4×C11C2×SD1612yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×Q811yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
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×Dic11C22⋊Q812yes—
302C2×Dic11C2×SD1612yes—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—48no—
308C4×D11—84no—
309Dic22—22no—
310Dic22—22no—
311Dic22—22no—
312Dic22—48no—
313Dic22C22⋊Q814yescomplemented
314C8×C11—41no—
315C8×C11—41no—
316C11⋊C8—22no—
317C11⋊C8—41no—
318C23×Q8—111no—
319C23×C8—111no—
320C2×C4⋊Q8C2×D1111yescharacteristic
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C22×C4⋊C4—111no—
325#475—224no—
326C2×#106—111no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106—111no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—224no—
339C2×#103C2×D1111yescharacteristic
340C2×#103C2×D1111yescharacteristic
341C2×C22⋊C8—111no—
342#398—221no—
343#395—221no—
344#391—111no—
345#391—221no—
346#391—221no—
347#391C2×D1111yescharacteristic
348#389—111no—
349#389—111no—
350#385—221no—
351#384—111no—
352#380—111no—
353#380—111no—
354#380—221no—
355C4×C22⋊C4—111no—
356C4×C22⋊C4—221no—
357#340—111no—
358#340—111no—
359#340C2×D1111yescharacteristic
360#340C2×D1111yescharacteristic
361#336—111no—
362#336C2×D1111yescharacteristic
363C22×C11C2×C22⋊Q811yescharacteristic
364C22×C11D4211yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11C22×SD1611yescharacteristic
367C22×C11C2×#13711yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57811yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11#47514yescomplemented
377C4×C11—22no—
378C4×C11—42no—
379C4×C11—41no—
380C4×C11—42no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11C2×C22⋊Q811yescharacteristic
384C4×C11#54311yescharacteristic
385C4×C11#54611yescharacteristic
386C4×C11#55111yescharacteristic
387Dic11—24no—
388Dic11—22no—
389Dic11—22no—
390Dic11—41no—
391Dic11—81no—
392Dic11—81no—
393Dic11—81no—
394C22×Q8—21no—
395C22×Q8—114no—
396C22×Q8—111no—
397C22×Q8—221no—
398C22×Q8—222no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—441no—
402C22×Q8—441no—
403C22×Q8C22×D1111yescharacteristic
404C23×C4—111no—
405C23×C4—221no—
406C23×C4—221no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—222no—
410C22×C8—222no—
411C22×C8—441no—
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414C4⋊Q8—22no—
415C4⋊Q8—41no—
416C22⋊Q8—444no—
417C4×Q8—222no—
418C4×Q8—222no—
419C4×Q8—441no—
420C4×Q8—441no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—441no—
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—111no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42C22×D1111yescharacteristic
445#106—222no—
446#106—222no—
447#106—441no—
448#106—441no—
449C4⋊C8—222no—
450C4⋊C8—441no—
451#103—22no—
452#103—41no—
453#103—114no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—222no—
458#103—441no—
459C22⋊C8—222no—
460#95—21no—
461#95—21no—
462#95—111no—
463#95—111no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11#243711yescharacteristic
471C2×C11C2×#47511yescharacteristic
472C2×C11#308211yescharacteristic
473C2×C11#327011yescharacteristic
474C2×C11D4×SD1611yescharacteristic
475C2×C11#329811yescharacteristic
476C2×C11#331611yescharacteristic
477D11—24no—
478C24—111no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—81no—
487C2×Q8—112no—
488C2×Q8—112no—
489C2×Q8—112no—
490C2×Q8—224no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—228no—
495C2×Q8—442no—
496C2×Q8—442no—
497C2×Q8—444no—
498C2×Q8—444no—
499C2×Q8—444no—
500C2×Q8Q8×D1112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—111no—
510C22×C4—224no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—442no—
523C22×C4—881no—
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—112no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—444no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4—881no—
559C4⋊C4D4×D1112yes—
560C22⋊C4—114no—
561C22⋊C4—222no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C42—21no—
565C42—21no—
566C42—221no—
567C42—221no—
568C42—442no—
569C42—442no—
570C11#2595511yescharacteristic, complemented, Sylow
571C23—112no—
572C23—112no—
573C23—112no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23C2×D4×D1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—84no—
584Q8—114no—
585Q8—222no—
586Q8—222no—
587Q8—222no—
588Q8—448no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—112no—
607C2×C4—112no—
608C2×C4—221no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—221no—
613C2×C4—222no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—448no—
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×C4SD16×D1112yes—
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4C2×Q8×D1111yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704211yescharacteristic
640C8—41no—
641C8—41no—
642C8—222no—
643C8—441no—
644C22—114no—
645C22—222no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—222no—
650C22—222no—
651C22#1062312111yescharacteristic
652C22D11×C22⋊Q811yescharacteristic
653C22#1062320711yescharacteristic
654C22C2×SD16×D1111yescharacteristic
655C22#1062329711yescharacteristic
656C22#1062330611yescharacteristic
657C22D11×#13711yescharacteristic
658C4—22no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—222no—
665C4—224no—
666C4—222no—
667C4—441no—
668C4—881no—
669C4—881no—
670C4—881no—
671C4D11×C22⋊Q811yescharacteristic
672C4#1062316511yescharacteristic
673C4#1062320711yescharacteristic
674C4#1062321011yescharacteristic
675C2—224no—
676C2#1307227611yescharacteristic
677C2D11×#47511yescharacteristic
678C2#1307845311yescharacteristic
679C2#1308018911yescharacteristic
680C2#1308031011yescharacteristic
681C2#1308048011yescharacteristic
682C2#1308072611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2024C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2024D11
hypocenterC11#25955
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
1. C2×#10622707C2semidirect
5. #13070157C2semidirect
6. #13069997C2semidirect
7. #13069993C2semidirect
8. #13068887C2semidirect
9. #13068885C2semidirect
13. #13068620C2semidirect
15. C11×#2024C2semidirect
68. C2×Q8×D11Q8semidirect
237. #2024D11semidirect
313. Dic22C22⋊Q8semidirect
376. C2×D11#475semidirect
570. C11#25955semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C2×D11×#1032
#130723142
#130714502
#130701572
#130699972
#130699932
#130688872
#130688852
#130688102
#130687952
#130686402
#130686202
#130685492
C11×#20242
#2595511