Finite Group Databasebeta

← #14781577

Subgroups — #14781577

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic, complemented
3#13077133C211yesmaximal, characteristic, complemented
4C2×#10622850C211yesmaximal, characteristic, complemented
5C2×#10622745C211yesmaximal, characteristic, complemented
6#13069883C212yesmaximal, complemented
7#13069878C212yesmaximal, complemented
8#13069876C212yesmaximal, complemented
9#13069871C212yesmaximal, complemented
10C2×#10622196C211yesmaximal, characteristic, complemented
11C11×#2896C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#67003—24no—
17C2×#67003—24no—
18C2×#67003—22no—
19C2×#67003—22no—
20C22×#4326C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C11×#419C2212yes—
28C11×#418C2212yes—
29C11×#417—22no—
30C11×#416—22no—
31#10622850—24no—
32C2×#66900C2212yes—
33C2×#66897C2212yes—
34C2×#66888C2212yes—
35#10622745—24no—
36C2×#66887C2212yes—
37#10622617C2212yes—
38#10622615—22no—
39#10622614C2212yes—
40#10622612—22no—
41#10622612C2212yes—
42#10622612C2212yes—
43#10622579—22no—
44C2×C4⋊(C11⋊C8)—22no—
45#10622196C2212yes—
46#10622196C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—22no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—22no—
54C2×C11×#41D414yes—
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C2×#4339—22no—
62C2×#4339—21no—
63C2×#4339—22no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—22no—
68C2×#4339D414yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22C2311yescharacteristic
72C2×C11×M16—21no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16C2312yes—
76C22×C8×C11—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117D412yes—
80C11×#117C2312yes—
81C2×C11×C4⋊C4D412yes—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84#67003—216no—
85#67003—216no—
86C2×#4326—22no—
87C2×#4326—22no—
88C2×#4326—22no—
89C2×#4325—22no—
90C2×#4325—22no—
91C2×#4325—22no—
92C2×#4324—22no—
93C2×#4324—22no—
94C2×#4324—22no—
95C2×#4323—22no—
96C2×#4323—22no—
97C2×#4323—22no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318—22no—
104C2×#4318C2312yes—
105C2×#4318C2312yes—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—22no—
108C22×C11⋊C8—21no—
109C22×C11⋊C8—21no—
110C22×C11⋊C8D412yes—
111C22×C11⋊C8D412yes—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C11×#103—24no—
115C11×#102—24no—
116#66900—24no—
117#66897—24no—
118#66888—24no—
119#66887—24no—
120#66874—24no—
121#66873—24no—
122C4⋊(C11⋊C8)—24no—
123C4⋊(C11⋊C8)—24no—
124#23520—111nomaximal, Sylow
125C24×C11—21no—
126C24×C11#4111yescharacteristic
127C23×D11—21no—
128C11×#41—24no—
129C11×#41—24no—
130C11×#41—24no—
131C11×#41—24no—
132C11×#41—42no—
133C11×#41—42no—
134C11×#41—42no—
135C11×#41—42no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11C2×D412yes—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—41no—
149C2×D4×C11—41no—
150C2×D4×C11—42no—
151C2×D4×C11C2×D412yes—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—42no—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—24no—
169C2×C22⋊D11—41no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—42no—
172C22×Dic11—21no—
173#4339—24no—
174#4339—24no—
175#4339—24no—
176#4339—24no—
177#4339—42no—
178#4339—42no—
179#4339—42no—
180#4339—42no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44C2×D412yes—
187C2×C4×D11—24no—
188C2×C4×D11—41no—
189C2×C4×D11—41no—
190C2×C4×D11—42no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22C2×D412yes—
197C11×M16—22no—
198C11×M16—22no—
199C11×M16—42no—
200C2×C8×C11—22no—
201C2×C8×C11—42no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4C2×D414yes—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C42×C11—22no—
207C42×C11—22no—
208#4326—28no—
209#4325—28no—
210#4324—28no—
211#4323—28no—
212#4318—22no—
213#4318—22no—
214#4318—22no—
215#4318—22no—
216#4318—42no—
217#4318—42no—
218C2×C11⋊C8—24no—
219C2×C11⋊C8—24no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—42no—
227C2×C11⋊C8—42no—
228C2×C11⋊C8C2×D412yes—
229C2×C11⋊C8C2×D412yes—
230C22×#135—111no—
231C2×#424—111no—
232#2896—111no—
233#2896D1111yescharacteristic, complemented
234C2×#413—111no—
235C2×#413—111no—
236#2047—112no—
237#2046—112no—
238#2046—112no—
239#2045—112no—
240C2×#341—111no—
241C23×C11—22no—
242C23×C11—42no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—82no—
246C23×C11#12111yescharacteristic
247C23×C11#12111yescharacteristic
248C23×C11#12312yes—
249C23×C11#12312yes—
250C23×C11C2×#4111yescharacteristic
251C22×D11—22no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—82no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—41no—
258Q8×C11—41no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—44no—
262D4×C11—44no—
263D4×C11—41no—
264D4×C11—41no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—44no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—44no—
271C2×C4×C11—44no—
272C2×C4×C11#12012yes—
273C2×C4×C11#12012yes—
274C2×C4×C11#12112yes—
275C2×C4×C11#12112yes—
276C2×C4×C11#12112yes—
277C2×C4×C11#12112yes—
278C2×C4×C11#12111yescharacteristic
279C2×C4×C11#12111yescharacteristic
280C2×C4×C11#12312yes—
281C2×C4×C11#12312yes—
282C2×C4×C11#12412yes—
283C2×C4×C11#12412yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C22⋊D11—44no—
291C22⋊D11—44no—
292C2×Dic11—22no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295D44—22no—
296D44—22no—
297D44—41no—
298D44—41no—
299C4×D11—44no—
300C4×D11—44no—
301Dic22—22no—
302Dic22—22no—
303Dic22—41no—
304Dic22—41no—
305C8×C11—42no—
306C11⋊C8—22no—
307C11⋊C8—22no—
308C11⋊C8—42no—
309C11⋊C8—42no—
310C22×#41—111no—
311C22×#41C2×D1111yescharacteristic
312C2×#135—222no—
313C2×#135—222no—
314C2×#135—224no—
315C2×#135—224no—
316C22×Q16—111no—
317C22×SD16—111no—
318C22×SD16—111no—
319C22×D8—111no—
320C22×M16—111no—
321C22×M16—111no—
322C22×M16C2×D1111yescharacteristic
323C23×C8—111no—
324C2×#117C2×D1111yescharacteristic
325#424—112no—
326#424—112no—
327#424—222no—
328C2×C4⋊C8—222no—
329#419—112no—
330#419C2×D1112yes—
331#418—112no—
332#418C2×D1112yes—
333#417—22no—
334#417—222no—
335#416—22no—
336#416—222no—
337#413—224no—
338#413—224no—
339C2×#101—112no—
340C2×#101—112no—
341C2×#100—112no—
342C2×#100—112no—
343#341—112no—
344#341—112no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—82no—
352C22×C11—82no—
353C22×C11—82no—
354C22×C11#39412yes—
355C22×C11#39412yes—
356C22×C11C2×#12111yescharacteristic
357C22×C11C2×#12311yescharacteristic
358C22×C11C2×#12311yescharacteristic
359C2×D11—42no—
360C2×D11—82no—
361C2×D11—82no—
362C2×D11—82no—
363C4×C11—42no—
364C4×C11—44no—
365C4×C11#39412yes—
366C4×C11#39412yes—
367C4×C11C2×#12011yescharacteristic
368C4×C11C2×#12111yescharacteristic
369C4×C11C2×#12111yescharacteristic
370C4×C11C2×#12411yescharacteristic
371Dic11—42no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—114no—
380C2×#41—222no—
381C2×#41—222no—
382C2×#41—221no—
383C2×#41—221no—
384C2×#41—222no—
385C2×#41—221no—
386C2×#41—221no—
387C2×#41D4414yes—
388C22×Q8—111no—
389C22×Q8C22×D1111yescharacteristic
390C22×D4—21no—
391C22×D4—111no—
392C22×D4—221no—
393C22×D4C22×D1111yescharacteristic
394C23×C4—21no—
395C23×C4—221no—
396C23×C4C22×D1111yescharacteristic
397#135—2216no—
398#135—2216no—
399C2×Q16—222no—
400C2×Q16—222no—
401C2×Q16—222no—
402C2×SD16—222no—
403C2×SD16—222no—
404C2×SD16—222no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×SD16—222no—
408C2×D8—222no—
409C2×D8—222no—
410C2×D8—222no—
411C2×M16—21no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—112no—
415C2×M16—112no—
416C2×M16—221no—
417C2×M16—221no—
418C2×M16—222no—
419C2×M16—222no—
420C2×M16—222no—
421C2×M16—222no—
422C2×M16C22×D1112yes—
423C22×C8—21no—
424C22×C8—112no—
425C22×C8—112no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8—222no—
429C22×C8—222no—
430C22×C8—221no—
431C22×C8—221no—
432#117—21no—
433#117—21no—
434#117C22⋊D1112yes—
435#117C22×D1112yes—
436C2×C4⋊C4C22⋊D1112yes—
437C2×C22⋊C4—21no—
438C2×C42—21no—
439C4⋊C8—224no—
440C4⋊C8—224no—
441#103—24no—
442#103—224no—
443#102—24no—
444#102—224no—
445#101—224no—
446#101—224no—
447#100—224no—
448#100—224no—
449C2×C11—21no—
450C2×C11—21no—
451C2×C11—22no—
452C2×C11—22no—
453C2×C11—82no—
454C2×C11C2×#39411yescharacteristic
455C2×C11#306712yes—
456D11—82no—
457C24—21no—
458C24—221no—
459C24#434111yescharacteristic
460#41—24no—
461#41—24no—
462#41—24no—
463#41—24no—
464#41—42no—
465#41—42no—
466#41—42no—
467#41—42no—
468#41—224no—
469#41—224no—
470#41—224no—
471#41—224no—
472#41—442no—
473#41—442no—
474#41—442no—
475#41—442no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—112no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8C2×D4412yes—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—112no—
498C2×D4—224no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—442no—
505C2×D4—441no—
506C2×D4—441no—
507C2×D4C2×D4412yes—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—42no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—221no—
515C22×C4—224no—
516C22×C4—442no—
517C22×C4—441no—
518C22×C4—441no—
519C22×C4C2×D4412yes—
520C22×C4#433912yes—
521C22×C4D4×D1112yes—
522C22×C4D4×D1111yescharacteristic
523C22×C4D4×D1111yescharacteristic
524C22×C4#434111yescharacteristic
525C22×C4#434112yes—
526C22×C4C2×C22⋊D1111yescharacteristic
527C22×C4C2×C22⋊D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529Q16—228no—
530SD16—228no—
531SD16—228no—
532D8—228no—
533M16—22no—
534M16—22no—
535M16—42no—
536M16—222no—
537M16—222no—
538M16—222no—
539M16—222no—
540M16—442no—
541M16—442no—
542C2×C8—22no—
543C2×C8—42no—
544C2×C8—112no—
545C2×C8—112no—
546C2×C8—224no—
547C2×C8—224no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—222no—
553C2×C8—222no—
554C2×C8—442no—
555C2×C8—442no—
556C4⋊C4—22no—
557C4⋊C4C2×C22⋊D1114yes—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C42—22no—
561C42—22no—
562C11#2352011yescharacteristic, complemented, Sylow
563C23—22no—
564C23—42no—
565C23—41no—
566C23—41no—
567C23—82no—
568C23—222no—
569C23—441no—
570C23—441no—
571C23—882no—
572C23#6693612yes—
573C23#6693912yes—
574C23#6699211yescharacteristic
575C23#6699211yescharacteristic
576C23C2×#434111yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581Q8—222no—
582Q8—222no—
583Q8—441no—
584Q8—441no—
585D4—22no—
586D4—22no—
587D4—44no—
588D4—44no—
589D4—41no—
590D4—41no—
591D4—222no—
592D4—222no—
593D4—444no—
594D4—444no—
595D4—441no—
596D4—441no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—44no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—222no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—444no—
608C2×C4—444no—
609C2×C4#6693512yes—
610C2×C4#6693512yes—
611C2×C4#6693612yes—
612C2×C4#6693812yes—
613C2×C4#6693812yes—
614C2×C4#6693912yes—
615C2×C4#6698312yes—
616C2×C4#6698312yes—
617C2×C4#6699112yes—
618C2×C4#6699112yes—
619C2×C4#6699211yescharacteristic
620C2×C4#6699211yescharacteristic
621C2×C4C22×D4411yescharacteristic
622C2×C4C2×#433911yescharacteristic
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4C2×D4×D1111yescharacteristic
625C2×C4C2×#434111yescharacteristic
626C2×C4C22×C22⋊D1111yescharacteristic
627C8—42no—
628C8—222no—
629C8—222no—
630C8—442no—
631C8—442no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—82no—
639C22—82no—
640C22—82no—
641C22—442no—
642C22—882no—
643C22—882no—
644C22—882no—
645C22#1062257412yes—
646C22#1062257412yes—
647C22C2×#6693611yescharacteristic
648C22C2×#6693911yescharacteristic
649C22C2×#6699211yescharacteristic
650C4—44no—
651C4—42no—
652C4—442no—
653C4#1062257412yes—
654C4#1062257412yes—
655C4C2×#6693511yescharacteristic
656C4C2×#6693811yescharacteristic
657C4C2×#6698311yescharacteristic
658C4C2×#6699111yescharacteristic
659C2—21no—
660C2—21no—
661C2—22no—
662C2—22no—
663C2—82no—
664C2—882no—
665C2C2×#1062257411yescharacteristic
666C2#1307833312yes—
subgroupG/H
centerC2×C4#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2896C2
socleC22×C11C2×#121
prime radicalC22×#67003C2
hypercenter#2896D11
hypocenterC11#23520
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. C2×#10622612C2semidirect
3. #13077133C2semidirect
4. C2×#10622850C2semidirect
5. C2×#10622745C2semidirect
6. #13069883C2semidirect
7. #13069878C2semidirect
8. #13069876C2semidirect
9. #13069871C2semidirect
10. C2×#10622196C2semidirect
11. C11×#2896C2semidirect
233. #2896D11semidirect
562. C11#23520semidirect

Maximal subgroups

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

subgroupindex
C22×#670032
C2×#106226122
#130771332
C2×#106228502
C2×#106227452
#130698832
#130698782
#130698762
#130698712
C2×#106221962
C11×#28962
#2352011