Finite Group Databasebeta

← #14782469

Subgroups — #14782469

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622608C211yesmaximal, characteristic, complemented
2C2×#10622731C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic
4C2×#10622579C211yesmaximal, characteristic
5#13071104C211yesmaximal, characteristic
6C2×#10622586C211yesmaximal, characteristic, complemented
7#13070012C212yesmaximal, complemented
8#13070005C212yesmaximal, complemented
9#13069998C212yesmaximal, complemented
10#13069991C212yesmaximal, complemented
11C11×#1736C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4—21no—
18C22×C4×Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×C11⋊#95—21no—
21#10622746—24no—
22#10622731—24no—
23C2×#66885C2212yes—
24C2×#66880C2212yes—
25C2×Dic11⋊C8C2212yes—
26C2×Dic11⋊C8C2212yes—
27#10622608—24no—
28#10622601C2211yescharacteristic
29#10622601C2211yescharacteristic
30#10622587C2211yescharacteristic
31#10622587C2211yescharacteristic
32#10622586—21no—
33#10622586—21no—
34#10622586C2212yes—
35#10622586C2212yes—
36C2×#66874C2212yes—
37#10622579—24no—
38C2×#66873C2212yes—
39C2×#66872C2212yes—
40C2×#66871C2212yes—
41#10622571—21no—
42#10622571—21no—
43C4×(C2×D11)⋊C4—21no—
44C4×(C2×D11)⋊C4—21no—
45C11×#340C2212yes—
46C11×#340C2212yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C23×Dic11—21no—
51C23×Dic11D411yescharacteristic
52C23×Dic11D411yescharacteristic
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339Q814yes—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2311yescharacteristic
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C22×C8×C11C2312yes—
66C11×#117—22no—
67C11×#117—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11D414yes—
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—44no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×#4318—22no—
94C2×#4318—22no—
95C2×#4318D414yes—
96C22×C11⋊C8C2312yes—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103#66885—24no—
104#66880—24no—
105Dic11⋊C8—24no—
106Dic11⋊C8—24no—
107#66874—24no—
108#66873—24no—
109#66872—24no—
110#66871—24no—
111#23617—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×Q812yes—
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—24no—
129C2×C22⋊D11—42no—
130C2×C22⋊D11—42no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—41no—
139C22×Dic11—41no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146#4339—28no—
147#4339—28no—
148#4339—44no—
149#4339—44no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C2×Q812yes—
156C2×C4×D11—24no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22C2×Q812yes—
165C11×M16—44no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C22⋊C4—42no—
177C42×C11—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182C4⋊Dic11—24no—
183C4⋊Dic11—22no—
184C4⋊Dic11C2×D414yes—
185Dic11⋊C4—44no—
186Dic11⋊C4—44no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193#4318—28no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8C2×D414yes—
197C2×#428—111no—
198C2×#423—111no—
199C2×#417—111no—
200C2×#417—111no—
201#2297—111no—
202C2×#389—111no—
203#2068—112no—
204#2067—112no—
205#2066—112no—
206#2065—112no—
207#1736D1111yescharacteristic, complemented
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11#12112yes—
213C23×C11#12112yes—
214C23×C11C22⋊Q812yes—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—84no—
233C2×C4×C11#12114yes—
234C2×C4×C11#12112yes—
235C2×C4×C11#12112yes—
236C2×C4×C11C22⋊Q814yes—
237C2×C4×C11C22⋊Q814yes—
238C2×C4×C11C22⋊Q812yes—
239C2×C4×C11#12614yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×Q811yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—48no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11—48no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11AGL(1,ℤ/8)12yes—
267C2×Dic11#13712yes—
268D44—22no—
269D44—22no—
270D44—41no—
271D44—41no—
272C4×D11—48no—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—42no—
278C11⋊C8—24no—
279C22×#41—111no—
280C22×M16—111no—
281C22×M16C2×D1111yescharacteristic
282C2×#117C2×D1111yescharacteristic
283C22×C4⋊C4—111no—
284C22×C4⋊C4—221no—
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C42—111no—
287#428—224no—
288C2×#107—112no—
289C2×#106—112no—
290#423—224no—
291C2×C4⋊C8—112no—
292C2×C4⋊C8—112no—
293#417—224no—
294#417—224no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#102—112no—
298C2×#102—112no—
299#391—111no—
300#391—111no—
301#390—111no—
302#390—111no—
303#389—112no—
304#389—112no—
305#389—221no—
306#389—221no—
307#386—221no—
308#386—221no—
309C4×C22⋊C4—221no—
310C4×C22⋊C4—221no—
311C2×#95—221no—
312#340C2×D1112yes—
313#340C2×D1112yes—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11#39614yes—
321C22×C11C2×#12111yescharacteristic
322C22×C11C2×#12111yescharacteristic
323C22×C11C2×C22⋊Q811yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11C2×#13711yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57511yescharacteristic
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—82no—
338C4×C11#39614yes—
339C4×C11C2×#12111yescharacteristic
340C4×C11C2×C22⋊Q811yescharacteristic
341C4×C11C2×C22⋊Q811yescharacteristic
342C4×C11C2×#12611yescharacteristic
343Dic11—22no—
344Dic11—22no—
345Dic11—42no—
346Dic11—44no—
347Dic11—41no—
348Dic11—41no—
349C2×#41—114no—
350C2×#41—222no—
351C2×#41—222no—
352C2×#41—222no—
353C2×#41—222no—
354C2×#41—222no—
355C22×Q8—111no—
356C22×D4—111no—
357C22×D4—221no—
358C23×C4—21no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—221no—
362C23×C4—221no—
363C23×C4C22×D1111yescharacteristic
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—114no—
368C2×M16—222no—
369C2×M16—222no—
370C22×C8—112no—
371C22×C8C22×D1112yes—
372#117—22no—
373#117—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—444no—
384C2×C4⋊C4C22×D1112yes—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—21no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—222no—
398C2×C42—222no—
399#107—224no—
400#106—224no—
401C4⋊C8—224no—
402C4⋊C8—224no—
403#103—224no—
404#103—224no—
405#102—224no—
406#102—224no—
407#95—222no—
408#95—222no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413C2×C11—24no—
414C2×C11C2×#39611yescharacteristic
415C2×C11#303611yescharacteristic
416C2×C11#303711yescharacteristic
417C2×C11#305511yescharacteristic
418C2×C11#305611yescharacteristic
419C2×C11#307911yescharacteristic
420C2×C11#308011yescharacteristic
421D11—82no—
422C24—221no—
423C24D4×D1111yescharacteristic
424#41—228no—
425#41—228no—
426#41—444no—
427#41—444no—
428C2×Q8—112no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×D4—112no—
435C2×D4—224no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—442no—
442C2×D4—442no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—224no—
461C22×C4—441no—
462C22×C4—441no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4#433912yes—
468C22×C4#433912yes—
469C22×C4#433912yes—
470C22×C4D4×D1111yescharacteristic
471C22×C4D4×D1112yes—
472C22×C4D4×D1112yes—
473C22×C4Q8×D1112yes—
474C22×C4C23×D1111yescharacteristic
475M16—44no—
476M16—228no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—114no—
481C2×C8—222no—
482C2×C8—222no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—114no—
491C4⋊C4—224no—
492C4⋊C4—222no—
493C4⋊C4—444no—
494C4⋊C4—444no—
495C22⋊C4—42no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—42no—
501C42—222no—
502C42—222no—
503C42—221no—
504C42—221no—
505C42—221no—
506C42—221no—
507C11#2361711yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—222no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23#6693712yes—
520C23#6693712yes—
521C23#6694912yes—
522C23C2×D4×D1111yescharacteristic
523Q8—222no—
524Q8—222no—
525Q8—441no—
526Q8—441no—
527D4—222no—
528D4—222no—
529D4—448no—
530D4—441no—
531D4—441no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—444no—
557C2×C4—444no—
558C2×C4—448no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—448no—
564C2×C4#6692914yes—
565C2×C4#6693714yes—
566C2×C4#6693712yes—
567C2×C4#6693712yes—
568C2×C4#6694914yes—
569C2×C4#6694914yes—
570C2×C4#6694912yes—
571C2×C4C2×#433911yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4C2×D4×D1111yescharacteristic
576C2×C4C2×Q8×D1111yescharacteristic
577C8—42no—
578C8—224no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—442no—
586C22—442no—
587C22—442no—
588C22—881no—
589C22—881no—
590C22—881no—
591C22—881no—
592C22#1062228914yes—
593C22C2×#6693711yescharacteristic
594C22C2×#6693711yescharacteristic
595C22C2×#6694911yescharacteristic
596C22D11×AGL(1,ℤ/8)11yescharacteristic
597C22#1062330411yescharacteristic
598C22D11×#13711yescharacteristic
599C22#1062330811yescharacteristic
600C4—81no—
601C4—81no—
602C4—82no—
603C4—222no—
604C4—222no—
605C4—444no—
606C4—441no—
607C4—442no—
608C4—441no—
609C4#1062228914yes—
610C4C2×#6692911yescharacteristic
611C4C2×#6693711yescharacteristic
612C4C2×#6694911yescharacteristic
613C4C2×#6694911yescharacteristic
614C2—24no—
615C2—882no—
616C2C2×#1062228911yescharacteristic
617C2#1307807911yescharacteristic
618C2#1307808711yescharacteristic
619C2#1307823311yescharacteristic
620C2#1307824411yescharacteristic
621C2#1307842911yescharacteristic
622C2#1307843711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#1736D11
hypocenterC11#23617
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
1. C2×#10622608C2semidirect
2. C2×#10622731C2semidirect
6. C2×#10622586C2semidirect
7. #13070012C2semidirect
8. #13070005C2semidirect
9. #13069998C2semidirect
10. #13069991C2semidirect
11. C11×#1736C2semidirect
207. #1736D11semidirect
507. C11#23617semidirect

Maximal subgroups

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

subgroupindex
C2×#106226082
C2×#106227312
C2×#106227462
C2×#106225792
#130711042
C2×#106225862
#130700122
#130700052
#130699982
#130699912
C11×#17362
#2361711