Finite Group Databasebeta

← #14767631

Subgroups — #14767631

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622803C211yesmaximal, characteristic
2#13071332C211yesmaximal, characteristic, complemented
3#13071330C211yesmaximal, characteristic
4#13069424C211yesmaximal, characteristic
5#13069416C211yesmaximal, characteristic, complemented
6#13068971C211yesmaximal, characteristic
7#13068970C211yesmaximal, characteristic
8#13068960C211yesmaximal, characteristic, complemented
9#13068959C211yesmaximal, characteristic, complemented
10#13068955C211yesmaximal, characteristic, complemented
11#13068951C211yesmaximal, characteristic
12#13068947C211yesmaximal, characteristic
13#13068748C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1878C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C22×#4314C2211yescharacteristic
24C2×#66946C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C11×#391C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622803C418yescomplemented
33C2×#66885C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622591—21no—
38#10622591—21no—
39#10622590C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622587C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622546—21no—
46#10622546—21no—
47#10622545C2211yescharacteristic
48#10622282—21no—
49#10622282—21no—
50#10622281—21no—
51#10622281—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×Dic22C2311yescharacteristic
65C2×C11×Q16—41no—
66C2×C11×Q16—41no—
67C2×C11×Q16C2×C414yescomplemented
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—41no—
71C4×Q8×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77#67000—22no—
78#67000C2×C414yes—
79Q8×Dic11—41no—
80Q8×Dic11—41no—
81#66997—22no—
82#66997C2×C414yescomplemented
83C2×#4326—41no—
84C2×#4326—41no—
85C2×#4326C2×C414yescomplemented
86C2×#4325—41no—
87C2×#4325—41no—
88C2×#4325C2×C414yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×#4314—41no—
109C2×#4314—41no—
110C2×#4314C2×C414yes—
111#66946—41no—
112#66946—41no—
113C4×Dic22—41no—
114C4×Dic22—41no—
115C11×#103—41no—
116C11×#103—41no—
117C11×#95—21no—
118C11×#95—21no—
119#66899—41no—
120#66899—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131#66885—41no—
132#66880—41no—
133#66879C2×C414yescomplemented
134C8×Dic11—22no—
135#66874—41no—
136#66873—41no—
137#22278—111nomaximal, Sylow
138C23×D11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
150C2×Q8×C11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44C22×C412yes—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22C22×C412yes—
180C11×Q16—44no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C22×C412yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—42no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—42no—
195#4326—44no—
196#4325—44no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201(C2×D11)⋊C4—81no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211Dic11⋊C4—81no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C4×Dic11—42no—
216C4×Dic11C22×C412yes—
217C4×Dic11#4112yes—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8C22×C412yes—
224#4314—44no—
225C2×#497—111no—
226#2327—111no—
227#2326—111no—
228#1958—111no—
229#1956—111no—
230#1880—111no—
231#1880—111no—
232#1878—111no—
233#1878—111no—
234#1878—111no—
235#1878D1111yescharacteristic, complemented
236#1877—111no—
237#1877—111no—
238#1836—111no—
239#1746—111no—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—41no—
255Q8×C11—41no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
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×C11C23×C411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
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×Dic11C4×D412yes—
300C2×Dic11C4×D412yes—
301D44—22no—
302D44—22no—
303D44—41no—
304D44—41no—
305C4×D11—84no—
306Dic22—22no—
307Dic22—22no—
308Dic22—41no—
309Dic22—41no—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—22no—
313C11⋊C8—41no—
314C22×Q16—111no—
315C22×Q16C2×D1111yescharacteristic
316C22×SD16—111no—
317C22×SD16—111no—
318C2×C4⋊Q8—111no—
319C2×#124—111no—
320C2×C4×Q8—111no—
321C2×C4×Q8—111no—
322C2×C4×Q8C2×D1111yescharacteristic
323C2×C4×D4—111no—
324#497—118no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103C2×D1111yescharacteristic
330C2×#103C2×D1111yescharacteristic
331C2×#102—111no—
332C2×#102—111no—
333C2×#97—111no—
334C2×C4×C8—111no—
335#391—111no—
336#391—111no—
337#391C2×D1111yescharacteristic
338#390—111no—
339#388—221no—
340#388—221no—
341#387—221no—
342#387—221no—
343#387—221no—
344#387—221no—
345#385—221no—
346#385—221no—
347#384—111no—
348#382—111no—
349#376—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340C2×D1111yescharacteristic
354#336—111no—
355#336—111no—
356#336—111no—
357#336C2×D1111yescharacteristic
358C22×C11C2×C4×D411yescharacteristic
359C22×C11#53511yescharacteristic
360C22×C11#53511yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57711yescharacteristic
363C22×C11#57811yescharacteristic
364C22×C11#57811yescharacteristic
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11#51811yescharacteristic
379C4×C11#51811yescharacteristic
380C4×C11#54011yescharacteristic
381C4×C11#54011yescharacteristic
382Dic11—22no—
383Dic11—22no—
384Dic11—42no—
385Dic11—41no—
386Dic11—41no—
387Dic11—81no—
388Dic11—81no—
389C22×Q8—111no—
390C22×Q8C22×D1111yescharacteristic
391C22×Q8C22×D1111yescharacteristic
392C22×D4—111no—
393C23×C4—221no—
394C2×Q16—41no—
395C2×Q16—41no—
396C2×Q16—114no—
397C2×Q16—441no—
398C2×Q16—441no—
399C2×Q16C4×D1114yescomplemented
400C2×SD16—114no—
401C2×SD16—114no—
402C2×SD16—441no—
403C2×SD16—441no—
404C2×SD16—441no—
405C2×SD16—441no—
406C22×C8—111no—
407C22×C8—111no—
408C22×C8C22×D1111yescharacteristic
409C22×C8C22×D1111yescharacteristic
410C4⋊Q8—114no—
411C4⋊Q8—222no—
412#124—114no—
413#124—222no—
414C4×Q8—41no—
415C4×Q8—41no—
416C4×Q8—441no—
417C4×Q8—441no—
418C4×Q8—441no—
419C4×Q8—441no—
420C4×D4—441no—
421C4×D4—441no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C42—21no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—221no—
442C2×C42—221no—
443C2×C42C22×D1111yescharacteristic
444#103—41no—
445#103—41no—
446#103—441no—
447#103—441no—
448#103—441no—
449#103—441no—
450#102—441no—
451#102—441no—
452#97—114no—
453C4×C8—222no—
454#95—21no—
455#95—21no—
456#95—111no—
457#95—111no—
458#95—111no—
459#95—111no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11#232811yescharacteristic
467C2×C11#294711yescharacteristic
468C2×C11#294711yescharacteristic
469C2×C11#322211yescharacteristic
470C2×C11#322311yescharacteristic
471C2×C11#322511yescharacteristic
472C2×C11#322511yescharacteristic
473D11—82no—
474C24—221no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—112no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8C2×C4×D1112yes—
492C2×Q8C2×C4×D1112yes—
493C2×D4—112no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—442no—
511C22×C4—881no—
512C22×C4—881no—
513C22×C4D4×D1111yescharacteristic
514C22×C4D4×D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516Q16—44no—
517Q16—444no—
518SD16—444no—
519SD16—444no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—112no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8C2×C4×D1112yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—881no—
546C4⋊C4—881no—
547C22⋊C4—224no—
548C22⋊C4—224no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C42—21no—
553C42—21no—
554C42—42no—
555C42—112no—
556C42—112no—
557C42—221no—
558C42—221no—
559C42—442no—
560C42—442no—
561C11#2227811yescharacteristic, complemented, Sylow
562C23—222no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23C2×D4×D1111yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—222no—
579Q8—222no—
580Q8—441no—
581Q8—441no—
582D4—222no—
583D4—222no—
584D4—441no—
585D4—441no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
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—112no—
605C2×C4—112no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—221no—
616C2×C4—221no—
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—884no—
626C2×C4C22×C4×D1111yescharacteristic
627C2×C4#6703711yescharacteristic
628C2×C4#6703711yescharacteristic
629C2×C4#6703711yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#6704211yescharacteristic
632C8—22no—
633C8—41no—
634C8—222no—
635C8—441no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22C4×D4×D1111yescharacteristic
644C22#1062312311yescharacteristic
645C22#1062313811yescharacteristic
646C22#1062329711yescharacteristic
647C22#1062330111yescharacteristic
648C22#1062330911yescharacteristic
649C22#1062331011yescharacteristic
650C4—41no—
651C4—41no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—222no—
657C4—222no—
658C4—441no—
659C4—441no—
660C4—442no—
661C4—881no—
662C4—881no—
663C4#1062301711yescharacteristic
664C4#1062307611yescharacteristic
665C4#1062314611yescharacteristic
666C4#1062319411yescharacteristic
667C2—882no—
668C2#1307133711yescharacteristic
669C2#1307745411yescharacteristic
670C2#1307745811yescharacteristic
671C2#1307968511yescharacteristic
672C2#1307969811yescharacteristic
673C2#1307972911yescharacteristic
674C2#1307973111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1878D11
hypocenterC11#22278
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. #13071332C2semidirect
5. #13069416C2semidirect
8. #13068960C2semidirect
9. #13068959C2semidirect
10. #13068955C2semidirect
13. #13068748C2semidirect
14. #13068366C2semidirect
15. C11×#1878C2semidirect
32. #10622803C4semidirect
67. C2×C11×Q16C2×C4semidirect
82. #66997C2×C4semidirect
85. C2×#4326C2×C4semidirect
133. #66879C2×C4semidirect
235. #1878D11semidirect
399. C2×Q16C4×D11semidirect
561. C11#22278semidirect

Maximal subgroups

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

subgroupindex
C2×#106228032
#130713322
#130713302
#130694242
#130694162
#130689712
#130689702
#130689602
#130689592
#130689552
#130689512
#130689472
#130687482
#130683662
C11×#18782
#2227811