Finite Group Databasebeta

← #14771009

Subgroups — #14771009

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×#10622416C211yesmaximal, characteristic
2#13071492C211yesmaximal, characteristic, complemented
3#13071445C211yesmaximal, characteristic
4#13069294C211yesmaximal, characteristic, complemented
5#13069260C211yesmaximal, characteristic, complemented
6#13069247C211yesmaximal, characteristic, complemented
7#13068878C211yesmaximal, characteristic, complemented
8#13068862C211yesmaximal, characteristic, complemented
9#13068701C211yesmaximal, characteristic, complemented
10#13068648C211yesmaximal, characteristic, complemented
11#13068555C211yesmaximal, characteristic
12#13068442C211yesmaximal, characteristic, complemented
13#13068430C211yesmaximal, characteristic, complemented
14#13068401C211yesmaximal, characteristic, complemented
15C11×#1935C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#389C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622600—21no—
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622591—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622416C418yescomplemented
46#10622279—21no—
47#10622278—21no—
48#10622278—21no—
49#10622277—21no—
50D11×#95—21no—
51#10622268—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C2×#4343—22no—
62C2×#4343—22no—
63C2×#4343—22no—
64C2×#4343—41no—
65C2×#4343—41no—
66C2×#4343C2×C414yes—
67C22×D44—21no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4313—41no—
98C2×#4313—41no—
99C2×#4313C2×C414yescomplemented
100#66946—22no—
101#66946—41no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11C2×C414yescomplemented
104C4×D44—22no—
105C4×D44—41no—
106C11×#103—41no—
107C11×#103C2×C414yescomplemented
108C11×#97—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112#66899—41no—
113#66899C2×C414yescomplemented
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66885—22no—
124#66885C2×C414yes—
125(C2×D11)⋊C8—22no—
126C8×Dic11—41no—
127#66873—22no—
128#66873C2×C414yes—
129#66872—41no—
130#66871—41no—
131#22578—111nomaximal, Sylow
132C23×D11—21no—
133C23×D11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C22×C412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153#4343—28no—
154#4343—44no—
155#4343—44no—
156#4343—44no—
157C2×D44—24no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44C22×C412yes—
164C2×D44#4112yes—
165C2×D44#4112yes—
166C2×C4×D11—24no—
167C2×C4×D11—24no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11—81no—
179C2×C4×D11—81no—
180C2×C4×D11—81no—
181C2×C4×D11—81no—
182C2×C4×D11C22×C412yes—
183C2×C4×D11#4112yes—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11C22×C412yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—81no—
196C11×C4⋊C4C22×C412yes—
197C42×C11—21no—
198C42×C11—21no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—42no—
204(C2×D11)⋊C4—81no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—81no—
211C4⋊Dic11C22×C412yes—
212Dic11⋊C4—24no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—81no—
216C4×Dic11—81no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C22×C412yes—
223#4313—44no—
224C2×#417—111no—
225#2345—111no—
226#2339—111no—
227#1935D1111yescharacteristic, complemented
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#1753—111no—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11C4×D412yes—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
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×C11—41no—
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
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×Dic11C4×D412yes—
299C2×Dic11#13712yes—
300D44—22no—
301D44—22no—
302D44—22no—
303D44—48no—
304D44#11714yes—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—22no—
308C4×D11—22no—
309C4×D11—48no—
310C4×D11—84no—
311C4×D11—84no—
312C4×D11—84no—
313C8×C11—22no—
314C8×C11—41no—
315C11⋊C8—22no—
316C11⋊C8—41no—
317C22×#41—111no—
318C22×M16—111no—
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×#103C2×D1111yescharacteristic
328C2×#103C2×D1111yescharacteristic
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×C22⋊C8—111no—
334C2×#97C2×D1111yescharacteristic
335C2×C4×C8—111no—
336#391—111no—
337#391C2×D1111yescharacteristic
338#389—111no—
339#389C2×D1111yescharacteristic
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—111no—
351C4×C22⋊C4—221no—
352C2×#95—221no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340C2×D1111yescharacteristic
358#340C2×D1111yescharacteristic
359#336—111no—
360#336—111no—
361C22×C11C2×C4×D411yescharacteristic
362C22×C11#54611yescharacteristic
363C22×C11#54611yescharacteristic
364C22×C11C2×#13711yescharacteristic
365C22×C11#57511yescharacteristic
366C22×C11#57611yescharacteristic
367C22×C11#57711yescharacteristic
368C2×D11—24no—
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—41no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—42no—
376C2×D11—41no—
377C2×D11—42no—
378C2×D11—41no—
379C2×D11—42no—
380C2×D11—41no—
381C2×D11—42no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—42no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11C2×#11711yescharacteristic
389C4×C11#51811yescharacteristic
390C4×C11#55111yescharacteristic
391C4×C11#55111yescharacteristic
392Dic11—22no—
393Dic11—22no—
394Dic11—42no—
395Dic11—41no—
396Dic11—81no—
397Dic11—81no—
398C2×#41—114no—
399C2×#41—222no—
400C2×#41—222no—
401C2×#41—222no—
402C2×#41—441no—
403C2×#41—441no—
404C22×Q8C22×D1111yescharacteristic
405C22×D4—111no—
406C22×D4—221no—
407C23×C4—111no—
408C23×C4—221no—
409C23×C4—221no—
410C23×C4—221no—
411C23×C4—221no—
412C2×M16—114no—
413C2×M16—441no—
414C2×M16—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—441no—
422C4×D4—441no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—111no—
441C2×C42—221no—
442C2×C42—221no—
443C2×C42C22×D1111yescharacteristic
444#107—441no—
445#106—441no—
446#103—41no—
447#103—114no—
448#103—441no—
449#103C4×D1114yescomplemented
450#102—114no—
451#102—114no—
452#102—222no—
453#102—222no—
454C22⋊C8—222no—
455#97—41no—
456C4×C8—441no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—111no—
461#95—111no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469C2×C11#234211yescharacteristic
470C2×C11C4×#13711yescharacteristic
471C2×C11#294611yescharacteristic
472C2×C11#330711yescharacteristic
473C2×C11#331411yescharacteristic
474C2×C11#332211yescharacteristic
475C2×C11#333111yescharacteristic
476D11—42no—
477D11—44no—
478C24—111no—
479C24—221no—
480#41—228no—
481#41—444no—
482#41—444no—
483#41—444no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C2×C4×D1112yes—
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—111no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—224no—
509C22×C4—224no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—442no—
523C22×C4—881no—
524C22×C4—881no—
525C22×C4—881no—
526C22×C4—881no—
527C22×C4D4×D1111yescharacteristic
528C22×C4D4×D1111yescharacteristic
529C22×C4C23×D1111yescharacteristic
530M16—444no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—112no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8C2×C4×D1112yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—81no—
549C4⋊C4—112no—
550C4⋊C4—224no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—881no—
557C4⋊C4C2×C4×D1112yes—
558C22⋊C4—222no—
559C22⋊C4—441no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—881no—
564C42—21no—
565C42—21no—
566C42—221no—
567C42—221no—
568C42—881no—
569C42—881no—
570C11#2257811yescharacteristic, complemented, Sylow
571C23—112no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23—221no—
576C23—222no—
577C23—222no—
578C23—221no—
579C23—222no—
580C23—221no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23C2×D4×D1111yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
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—21no—
602C2×C4—21no—
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—112no—
614C2×C4—112no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—222no—
626C2×C4—221no—
627C2×C4—448no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—884no—
637C2×C4—884no—
638C2×C4—884no—
639C2×C4C22×C4×D1111yescharacteristic
640C2×C4#6703711yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#6704211yescharacteristic
645C8—22no—
646C8—41no—
647C8—222no—
648C8—441no—
649C22—222no—
650C22—224no—
651C22—222no—
652C22—222no—
653C22—441no—
654C22—442no—
655C22—441no—
656C22—442no—
657C22—442no—
658C22—441no—
659C22—442no—
660C22—442no—
661C22—442no—
662C22—441no—
663C22C4×D4×D1111yescharacteristic
664C22#1062314111yescharacteristic
665C22#1062320711yescharacteristic
666C22#1062330511yescharacteristic
667C22D11×#13711yescharacteristic
668C22#1062330811yescharacteristic
669C22#1062330911yescharacteristic
670C4—41no—
671C4—42no—
672C4—42no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—222no—
677C4—222no—
678C4—441no—
679C4—442no—
680C4—881no—
681C4—881no—
682C4D11×#11711yescharacteristic
683C4#1062307611yescharacteristic
684C4#1062319011yescharacteristic
685C4#1062323611yescharacteristic
686C2—442no—
687C2—444no—
688C2#1307146411yescharacteristic
689C2#1307743211yescharacteristic
690C2#1307744711yescharacteristic
691C2#1308059111yescharacteristic
692C2#1308069611yescharacteristic
693C2#1308082311yescharacteristic
694C2#1308092711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1935C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
cosocleC22×C4×C11C24
hypercenter#1935D11
hypocenterC11#22578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
2. #13071492C2semidirect
4. #13069294C2semidirect
5. #13069260C2semidirect
6. #13069247C2semidirect
7. #13068878C2semidirect
8. #13068862C2semidirect
9. #13068701C2semidirect
10. #13068648C2semidirect
12. #13068442C2semidirect
13. #13068430C2semidirect
14. #13068401C2semidirect
15. C11×#1935C2semidirect
45. #10622416C4semidirect
99. C2×#4313C2×C4semidirect
103. C4⋊C4×D11C2×C4semidirect
107. C11×#103C2×C4semidirect
113. #66899C2×C4semidirect
227. #1935D11semidirect
449. #103C4×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×#106224162
#130714922
#130714452
#130692942
#130692602
#130692472
#130688782
#130688622
#130687012
#130686482
#130685552
#130684422
#130684302
#130684012
C11×#19352
#2257811