Finite Group Databasebeta

← #14771007

Subgroups — #14771007

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622746C211yesmaximal, characteristic
2#13071491C211yesmaximal, characteristic, complemented
3#13071447C211yesmaximal, characteristic
4#13069306C211yesmaximal, characteristic, complemented
5#13069292C211yesmaximal, characteristic, complemented
6#13069258C211yesmaximal, characteristic, complemented
7#13069251C211yesmaximal, characteristic, complemented
8#13068880C211yesmaximal, characteristic, complemented
9#13068866C211yesmaximal, characteristic, complemented
10#13068703C211yesmaximal, characteristic, complemented
11#13068649C211yesmaximal, characteristic, complemented
12#13068557C211yesmaximal, characteristic
13#13068442C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25#10622825C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622746C418yescomplemented
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38#10622569—21no—
39#10622569—21no—
40#10622555—21no—
41C22⋊C4×Dic11—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622277—21no—
49D11×#95—21no—
50#10622267—21no—
51#10622267—21no—
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339C2×C414yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×Dic22C2311yescharacteristic
74C2×C11×M16—41no—
75C2×C11×M16—41no—
76C2×C11×M16C2×C414yescomplemented
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11C2×C414yescomplemented
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C4×D44—22no—
103C4×D44—22no—
104C4×D44—41no—
105C4×D44—41no—
106C11×C22⋊C8—22no—
107C11×#97—41no—
108C4×C8×C11—41no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66885—22no—
122#66885—22no—
123#66885C2×C414yes—
124#66885C2×C414yes—
125#66882—41no—
126#66881—41no—
127#66880—41no—
128#66880—41no—
129#66880C2×C414yescomplemented
130#66880C2×C414yescomplemented
131#22578—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C23×D11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—24no—
147C2×C22⋊D11—42no—
148C2×C22⋊D11—42no—
149C22×Dic11—24no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—81no—
158C22×Dic11—81no—
159#4339—28no—
160#4339—44no—
161#4339—44no—
162#4339—44no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44C22×C412yes—
167C2×D44#4112yes—
168C2×D44#4112yes—
169C2×C4×D11—24no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—81no—
177C2×C4×D11—81no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22C22×C412yes—
184C11×M16—44no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11C22×C412yes—
196C2×C8×C11C22×C412yes—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—41no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C22⋊Dic11—42no—
204C22⋊Dic11—81no—
205(C2×D11)⋊C4—42no—
206(C2×D11)⋊C4—42no—
207C4⋊Dic11—24no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11C22×C412yes—
219C4⋊Dic11C22×C412yes—
220Dic11⋊C4—81no—
221Dic11⋊C4—81no—
222C4×Dic11—81no—
223C4×Dic11—81no—
224C2×#417—111no—
225#2345—111no—
226#2339—111no—
227#1935—111no—
228#1933—111no—
229#1928—111no—
230#1927—111no—
231#1864—111no—
232#1862—111no—
233#1823—111no—
234#1809—111no—
235#1788—111no—
236#1762—111no—
237C4×#102—111no—
238#1753D1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11C4×D412yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
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—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11C4×D412yes—
272C2×C4×C11#13712yes—
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C22⋊D11—48no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
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×Dic11—84no—
302D44—22no—
303D44—22no—
304D44—22no—
305D44#11714yes—
306C4×D11—48no—
307C4×D11—84no—
308C4×D11—84no—
309Dic22—22no—
310Dic22—22no—
311Dic22—41no—
312Dic22—41no—
313C8×C11—22no—
314C8×C11—22no—
315C8×C11—41no—
316C8×C11—41no—
317C22×#41—111no—
318C22×M16C2×D1111yescharacteristic
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C22×C4⋊C4—111no—
322C2×#107—111no—
323C2×#106—111no—
324#417—118no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×C22⋊C8C2×D1111yescharacteristic
334C2×#97C2×D1111yescharacteristic
335C2×C4×C8C2×D1111yescharacteristic
336#391—111no—
337#391—111no—
338#389—111no—
339#389—111no—
340#387—221no—
341#387—221no—
342#386—221no—
343#386—221no—
344#381—221no—
345#380—111no—
346#380—111no—
347#380—221no—
348C4×C4⋊C4—111no—
349C4×C4⋊C4—111no—
350C4×C22⋊C4—221no—
351C4×C22⋊C4C2×D1111yescharacteristic
352C2×#95—221no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#336C2×D1111yescharacteristic
360#336C2×D1111yescharacteristic
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11C2×C4×D411yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11#54611yescharacteristic
371C22×C11C2×#13711yescharacteristic
372C22×C11#57511yescharacteristic
373C22×C11#57611yescharacteristic
374C22×C11#57711yescharacteristic
375C2×D11—24no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C2×D11—42no—
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11C2×#11711yescharacteristic
388C4×C11#51811yescharacteristic
389C4×C11#55111yescharacteristic
390C4×C11#55111yescharacteristic
391Dic11—42no—
392Dic11—42no—
393Dic11—42no—
394Dic11—81no—
395Dic11—81no—
396Dic11—81no—
397Dic11—81no—
398C2×#41—114no—
399C2×#41—222no—
400C2×#41—222no—
401C2×#41—222no—
402C2×#41—441no—
403C2×#41—441no—
404C22×Q8—111no—
405C22×D4—111no—
406C22×D4—221no—
407C23×C4—221no—
408C23×C4—221no—
409C23×C4—221no—
410C23×C4—221no—
411C23×C4C22×D1111yescharacteristic
412C2×M16—41no—
413C2×M16—41no—
414C2×M16C4×D1114yescomplemented
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—441no—
422C4×D4—441no—
423C2×C4⋊C4—114no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4D4411yescharacteristic
439C2×C22⋊C4D4411yescharacteristic
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1111yescharacteristic
444#107—441no—
445#106—441no—
446#103—114no—
447#103—114no—
448#103—441no—
449#103—441no—
450#102—114no—
451#102—114no—
452#102—222no—
453#102—222no—
454C22⋊C8—22no—
455#97—41no—
456C4×C8—41no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95D4411yescharacteristic
468#95D4411yescharacteristic
469C2×C11—42no—
470C2×C11#234211yescharacteristic
471C2×C11C4×#13711yescharacteristic
472C2×C11#294611yescharacteristic
473C2×C11#330711yescharacteristic
474C2×C11#331411yescharacteristic
475C2×C11#332211yescharacteristic
476C2×C11#333111yescharacteristic
477D11—44no—
478C24—221no—
479C24C2×D4411yescharacteristic
480#41—228no—
481#41—444no—
482#41—444no—
483#41—444no—
484C2×Q8—112no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×D4—112no—
491C2×D4—112no—
492C2×D4—112no—
493C2×D4—224no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—442no—
498C2×D4—442no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—881no—
519C22×C4—881no—
520C22×C4—881no—
521C22×C4—881no—
522C22×C4C2×C4×D1112yes—
523C22×C4C2×D4411yescharacteristic
524C22×C4C2×D4411yescharacteristic
525C22×C4C2×D4411yescharacteristic
526C22×C4C2×D4411yescharacteristic
527C22×C4C2×D4411yescharacteristic
528C22×C4#433912yes—
529C22×C4C23×D1111yescharacteristic
530M16—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8C2×C4×D1112yes—
542C2×C8C2×C4×D1112yes—
543C4⋊C4—112no—
544C4⋊C4—112no—
545C4⋊C4—224no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—881no—
557C4⋊C4—881no—
558C22⋊C4—22no—
559C22⋊C4—41no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—881no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—881no—
569C42—881no—
570C11#2257811yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—222no—
578C23—222no—
579C23—222no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23C4×D4412yes—
585C23C22×D4411yescharacteristic
586Q8—222no—
587Q8—222no—
588Q8—441no—
589Q8—441no—
590D4—114no—
591D4—222no—
592D4—222no—
593D4—222no—
594D4—448no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—448no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
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—441no—
633C2×C4—441no—
634C2×C4—884no—
635C2×C4—884no—
636C2×C4—884no—
637C2×C4C4×D4412yes—
638C2×C4#6696212yes—
639C2×C4C22×C4×D1111yescharacteristic
640C2×C4C2×#433911yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#41×D1111yescharacteristic
645C8—22no—
646C8—22no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—224no—
657C22—442no—
658C22—442no—
659C22—442no—
660C22—442no—
661C22—442no—
662C22—442no—
663C22C2×C4×D4411yescharacteristic
664C22#1062308511yescharacteristic
665C22#1062308511yescharacteristic
666C22C2×#6696211yescharacteristic
667C22#1062327911yescharacteristic
668C22#1062328211yescharacteristic
669C22#1062328311yescharacteristic
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—442no—
676C4—442no—
677C4—442no—
678C4—881no—
679C4—881no—
680C4—881no—
681C4—881no—
682C4#1062301711yescharacteristic
683C4D11×#11711yescharacteristic
684C4#1062308711yescharacteristic
685C4#1062308711yescharacteristic
686C2—42no—
687C2—444no—
688C2#1307146811yescharacteristic
689C2C4×#6696211yescharacteristic
690C2#1307745011yescharacteristic
691C2#1308059411yescharacteristic
692C2#1308069911yescharacteristic
693C2#1308081911yescharacteristic
694C2#1308093311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. #13071491C2semidirect
4. #13069306C2semidirect
5. #13069292C2semidirect
6. #13069258C2semidirect
7. #13069251C2semidirect
8. #13068880C2semidirect
9. #13068866C2semidirect
10. #13068703C2semidirect
11. #13068649C2semidirect
13. #13068442C2semidirect
14. C4×#66885C2semidirect
15. C11×#1753C2semidirect
27. #10622746C4semidirect
76. C2×C11×M16C2×C4semidirect
91. C2×C4⋊Dic11C2×C4semidirect
129. #66880C2×C4semidirect
130. #66880C2×C4semidirect
238. #1753D11semidirect
414. C2×M16C4×D11semidirect
570. C11#22578semidirect

Maximal subgroups

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

subgroupindex
C2×#106227462
#130714912
#130714472
#130693062
#130692922
#130692582
#130692512
#130688802
#130688662
#130687032
#130686492
#130685572
#130684422
C4×#668852
C11×#17532
#2257811