Finite Group Databasebeta

← #14780620

Subgroups — #14780620

Order 2816.

2170 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C22×#66977C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4C2×#10622617C211yesmaximal, characteristic, complemented
5C2×#10622820C211yesmaximal, characteristic, complemented
6#13069624C214yesmaximal, complemented
7#13069619C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C2×C11×#525C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C11×#525—24no—
14C11×#525—24no—
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8C2212yes—
17C2×C11×#121C2212yes—
18C2×C11×#120—21no—
19C2×C4×D4×C11—22no—
20C2×C11×#117C2211yescharacteristic
21C22×C22⋊Dic11—21no—
22C2×#67004—24no—
23C2×#67004—24no—
24C2×#67004—24no—
25C22×#4326C2212yescomplemented
26C22×#4324C2212yescomplemented
27C22×C4⋊Dic11C2211yescharacteristic
28C2×#66977—22no—
29C2×#66977—24no—
30C2×#66977—24no—
31C2×#66977C2214yes—
32C22×Dic11⋊C4—21no—
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35#10622845—24no—
36C2×#66899C2212yescomplemented
37C2×#66896C2212yescomplemented
38#10622820—24no—
39C2×C22⋊(C11⋊C8)C2214yes—
40#10622617—24no—
41C2×#66874C2214yescomplemented
42#10622167C2214yescomplemented
43C25×C11D411yescharacteristic
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41D414yes—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—21no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D412yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C23×Dic11—21no—
67C22×Dic22—22no—
68C22×Dic22—22no—
69C22×Dic22—22no—
70C22×Dic22—22no—
71C22×Dic22—22no—
72C22×Dic22—21no—
73C22×Dic22D414yescomplemented
74C22×Dic22C2312yes—
75C11×#123—28no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—24no—
78C11×#121—24no—
79C11×#121—24no—
80C11×#120—28no—
81C4×D4×C11—216no—
82C11×#117—22no—
83C11×#117D414yes—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C42×C11—21no—
90C2×C22⋊Dic11—28no—
91C2×C22⋊Dic11—24no—
92#67004—232no—
93C2×#4326—24no—
94C2×#4326—24no—
95C2×#4326—24no—
96C2×#4324—24no—
97C2×#4324—24no—
98C2×#4324—24no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11D414yescomplemented
102C2×C4⋊Dic11C2312yes—
103#66977—216no—
104#66977—28no—
105#66977—28no—
106C2×Dic11⋊C4—28no—
107C2×Dic11⋊C4—24no—
108C2×#4318—22no—
109C2×#4318—22no—
110C2×#4318—22no—
111C2×#4318—22no—
112C2×#4318—22no—
113C2×#4318D414yescomplemented
114C22×C11⋊C8C2312yes—
115C22×C11⋊C8C2312yes—
116#66899—24no—
117#66896—24no—
118C22⋊(C11⋊C8)—28no—
119#66874—28no—
120#23392—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11—24no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—21no—
126C24×C11—42no—
127C24×C11C2×D412yes—
128C24×C11C2×D411yescharacteristic
129C11×#41—28no—
130C11×#41—28no—
131C11×#41—44no—
132C11×#41—44no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—28no—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—44no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—44no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—44no—
167C22×C4×C11—42no—
168C22×C4×C11—44no—
169C22×C4×C11—44no—
170C22×C4×C11—42no—
171C22×C4×C11—44no—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11#4112yes—
180C22×C4×C11C2411yescharacteristic
181C22×Dic11—24no—
182C22×Dic11—24no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—44no—
186C22×Dic11—42no—
187C22×Dic11—42no—
188C2×Dic22—28no—
189C2×Dic22—24no—
190C2×Dic22—28no—
191C2×Dic22—22no—
192C2×Dic22—22no—
193C2×Dic22—22no—
194C2×Dic22—22no—
195C2×Dic22—22no—
196C2×Dic22—42no—
197C2×Dic22—44no—
198C2×Dic22—42no—
199C2×Dic22—44no—
200C2×Dic22C2×D414yes—
201C11×C4⋊C4—28no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4C2×D414yes—
204C11×C22⋊C4—28no—
205C11×C22⋊C4—28no—
206C11×C22⋊C4—24no—
207C42×C11—24no—
208C22⋊Dic11—216no—
209#4326—216no—
210#4324—216no—
211C4⋊Dic11—24no—
212C4⋊Dic11—22no—
213C4⋊Dic11C2×D414yes—
214Dic11⋊C4—216no—
215#4318—28no—
216#4318—44no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8C2×D414yes—
223C22×#137—111no—
224C2×#525D1111yescharacteristic
225C22×C22⋊Q8—111no—
226C2×#417—111no—
227C2×#419—111no—
228C2×#407—111no—
229#2001—114no—
230#2000—114no—
231#1736—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—28no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—48no—
243C23×C11—48no—
244C23×C11—44no—
245C23×C11—44no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11#12012yes—
251C23×C11#12012yes—
252C23×C11#12112yes—
253C23×C11#13714yescomplemented
254C23×C11C22×D411yescharacteristic
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—41no—
258Q8×C11—41no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—416no—
262D4×C11—48no—
263D4×C11—41no—
264D4×C11—41no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—44no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—48no—
280C2×C4×C11—48no—
281C2×C4×C11#12014yes—
282C2×C4×C11#12012yes—
283C2×C4×C11#12012yes—
284C2×C4×C11#12114yes—
285C2×C4×C11#12114yes—
286C2×C4×C11#12112yes—
287C2×C4×C11#12714yes—
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×Dic11—24no—
295C2×Dic11—24no—
296C2×Dic11—48no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—44no—
300C2×Dic11—48no—
301Dic22—24no—
302Dic22—24no—
303Dic22—42no—
304Dic22—42no—
305Dic22—48no—
306C11⋊C8—24no—
307C11⋊C8—42no—
308C22×#41C2×D1111yescharacteristic
309C23×Q8—111no—
310C24×C4C2×D1111yescharacteristic
311C2×#137—224no—
312C2×#137—224no—
313C2×#137—224no—
314C22×Q16—112no—
315C22×SD16—112no—
316C22×M16—111no—
317C22×M16—111no—
318#525—24no—
319#525—24no—
320C2×#123—21no—
321C2×C22⋊Q8—114no—
322C2×C22⋊Q8—224no—
323C2×C22⋊Q8—224no—
324C2×C22⋊Q8—222no—
325C2×C22⋊Q8C2×D1112yes—
326C2×#121C2×D1112yes—
327C2×#120—21no—
328C2×C4×D4—22no—
329C2×#117C2×D1111yescharacteristic
330C22×C4⋊C4—111no—
331C22×C4⋊C4—221no—
332C22×C22⋊C4—221no—
333#419—224no—
334#417—224no—
335C2×#103—112no—
336C2×#103—114no—
337C2×#102—112no—
338#407—224no—
339C2×C22⋊C8—114no—
340#340—114no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—24no—
344C22×C11—24no—
345C22×C11—24no—
346C22×C11—24no—
347C22×C11—24no—
348C22×C11—416no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—44no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—82no—
358C22×C11#39214yes—
359C22×C11C2×#12011yescharacteristic
360C22×C11C2×#12011yescharacteristic
361C22×C11C2×#12111yescharacteristic
362C22×C11C2×#13712yes—
363C22×C11#57512yes—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—44no—
367C4×C11#39214yes—
368C4×C11C2×#12011yescharacteristic
369C4×C11C2×#12111yescharacteristic
370C4×C11C2×#12111yescharacteristic
371C4×C11C2×#12711yescharacteristic
372Dic11—44no—
373Dic11—44no—
374C25C22⋊D1111yescharacteristic
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41C22⋊D1114yes—
381C22×Q8—114no—
382C22×Q8—112no—
383C22×Q8—222no—
384C22×Q8—221no—
385C22×Q8—222no—
386C22×Q8—222no—
387C22×Q8—222no—
388C22×Q8—222no—
389C22×Q8C22×D1111yescharacteristic
390C22×D4—22no—
391C22×D4—21no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—21no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—221no—
401C23×C4—221no—
402C23×C4C22⋊D1111yescharacteristic
403C23×C4C22⋊D1112yes—
404C23×C4C22×D1112yes—
405C23×C4C22×D1111yescharacteristic
406#137—2232no—
407C2×Q16—224no—
408C2×Q16—224no—
409C2×Q16—224no—
410C2×SD16—224no—
411C2×SD16—224no—
412C2×SD16—224no—
413C2×M16—114no—
414C2×M16—222no—
415C2×M16—222no—
416C2×M16—222no—
417C2×M16—222no—
418C2×M16—222no—
419C22×C8—112no—
420C22×C8—112no—
421#123—28no—
422C22⋊Q8—24no—
423C22⋊Q8—24no—
424C22⋊Q8—228no—
425C22⋊Q8—228no—
426C22⋊Q8—2216no—
427#121—24no—
428#121—24no—
429#120—28no—
430C4×D4—216no—
431#117—22no—
432#117C22⋊D1114yes—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—228no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—224no—
440C2×C4⋊C4C22×D1112yes—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—228no—
445C2×C22⋊C4—224no—
446C2×C42—21no—
447#103—224no—
448#103—228no—
449#102—224no—
450C22⋊C8—228no—
451C2×C11—24no—
452C2×C11—44no—
453C2×C11—82no—
454C2×C11C2×#39211yescharacteristic
455C2×C11#300411yescharacteristic
456C2×C11#300511yescharacteristic
457C2×C11#300712yes—
458C2×C11#305612yes—
459C24—22no—
460C24—24no—
461C24—22no—
462C24—22no—
463C24—21no—
464C24—42no—
465C24C2×C22⋊D1112yes—
466C24C2×C22⋊D1111yescharacteristic
467#41—28no—
468#41—28no—
469#41—44no—
470#41—44no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—114no—
477C2×Q8—224no—
478C2×Q8—222no—
479C2×Q8—228no—
480C2×Q8—228no—
481C2×Q8—222no—
482C2×Q8—222no—
483C2×Q8—222no—
484C2×Q8—222no—
485C2×Q8—442no—
486C2×Q8—444no—
487C2×Q8—444no—
488C2×Q8—442no—
489C2×Q8C2×C22⋊D1112yes—
490C2×D4—28no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—44no—
501C2×D4C2×C22⋊D1112yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—44no—
518C22×C4—42no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—42no—
522C22×C4—44no—
523C22×C4—224no—
524C22×C4—224no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—444no—
528C22×C4—442no—
529C22×C4—442no—
530C22×C4D4×D1112yes—
531C22×C4D4×D1112yes—
532C22×C4D4×D1112yes—
533C22×C4#434112yes—
534C22×C4C2×C22⋊D1112yes—
535C22×C4C2×C22⋊D1111yescharacteristic
536C22×C4C2×C22⋊D1112yes—
537C22×C4C2×C22⋊D1112yes—
538C22×C4C23×D1111yescharacteristic
539Q16—2216no—
540SD16—2216no—
541M16—228no—
542M16—444no—
543C2×C8—114no—
544C2×C8—222no—
545C2×C8—222no—
546C2×C8—222no—
547C2×C8—222no—
548C2×C8—222no—
549C4⋊C4—28no—
550C4⋊C4—22no—
551C4⋊C4—114no—
552C4⋊C4—2216no—
553C4⋊C4—224no—
554C4⋊C4—222no—
555C4⋊C4C2×C22⋊D1114yes—
556C22⋊C4—28no—
557C22⋊C4—28no—
558C22⋊C4—24no—
559C22⋊C4—2216no—
560C42—24no—
561C11#2339211yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—28no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—48no—
573C23—48no—
574C23—44no—
575C23—44no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—42no—
580C23#6699012yes—
581C23#6699212yes—
582C23#6700414yescomplemented
583C23#6700612yes—
584C23C22×C22⋊D1111yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589Q8—224no—
590Q8—224no—
591Q8—442no—
592Q8—442no—
593Q8—448no—
594D4—22no—
595D4—22no—
596D4—416no—
597D4—48no—
598D4—41no—
599D4—41no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—44no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—48no—
615C2×C4—48no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—448no—
619C2×C4—442no—
620C2×C4—448no—
621C2×C4—444no—
622C2×C4—442no—
623C2×C4#6699014yes—
624C2×C4#6699012yes—
625C2×C4#6699114yes—
626C2×C4#6699214yes—
627C2×C4#6699212yes—
628C2×C4#6699314yes—
629C2×C4#6700612yes—
630C2×C4C2×D4×D1111yescharacteristic
631C2×C4C2×D4×D1111yescharacteristic
632C2×C4C2×D4×D1111yescharacteristic
633C2×C4C2×#434111yescharacteristic
634C2×C4C22×C22⋊D1111yescharacteristic
635C2×C4C22×C22⋊D1111yescharacteristic
636C8—224no—
637C8—442no—
638C22—22no—
639C22—22no—
640C22—24no—
641C22—24no—
642C22—24no—
643C22—24no—
644C22—24no—
645C22—416no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—44no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—82no—
655C22#1062283614yes—
656C22C2×#6699011yescharacteristic
657C22C2×#6699211yescharacteristic
658C22#1062335312yes—
659C22C2×#6700412yes—
660C22C2×#6700611yescharacteristic
661C4—44no—
662C4—42no—
663C4—42no—
664C4—444no—
665C4—444no—
666C4#1062283614yes—
667C4C2×#6699011yescharacteristic
668C4C2×#6699111yescharacteristic
669C4C2×#6699211yescharacteristic
670C4C2×#6699311yescharacteristic
671C2—24no—
672C2—44no—
673C2—82no—
674C2C2×#1062283611yescharacteristic
675C2#1307784911yescharacteristic
676C2#1307785611yescharacteristic
677C2#1307787612yes—
678C2#1307824812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC23×C11C22×D4
hypercenterC2×#525D11
hypocenterC11#23392
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C22×#66977C2semidirect
3. C2×#10622845C2semidirect
4. C2×#10622617C2semidirect
5. C2×#10622820C2semidirect
6. #13069624C2semidirect
7. #13069619C2semidirect
8. #13068337C2semidirect
25. C22×#4326C22semidirect
26. C22×#4324C22semidirect
36. C2×#66899C22semidirect
37. C2×#66896C22semidirect
41. C2×#66874C22semidirect
42. #10622167C22semidirect
73. C22×Dic22D4semidirect
101. C2×C4⋊Dic11D4semidirect
113. C2×#4318D4semidirect
253. C23×C11#137semidirect
561. C11#23392semidirect
582. C23#67004semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#669772
C2×#106228452
C2×#106226172
C2×#106228202
#130696242
#130696192
#130683372
C2×C11×#5252
#2339211