Finite Group Databasebeta

← #104×Dic22 #14770470

Subgroups — #104×Dic22 #14770470

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic22C211yesmaximal, characteristic
2M16×Dic22C211yesmaximal, characteristic, complemented
3C42×Dic22C211yesmaximal, characteristic, complemented
4#13069593C211yesmaximal, characteristic, complemented
5#13069591C212yesmaximal, complemented
6#13069560C211yesmaximal, characteristic, complemented
7#13069558C212yesmaximal, complemented
8#13068636C211yesmaximal, characteristic
9#13068634C212yesmaximal
10#104×Dic11C212yesmaximal
11C4×C11×#104C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13#41×Dic11C2212yes—
14#10623101C411yescharacteristic, complemented
15#10623100C412yescomplemented
16Q8×Dic22C411yescharacteristic, complemented
17#10623074—21no—
18#10623074C411yescharacteristic, complemented
19#10623070—22no—
20#10623070C412yescomplemented
21D4×Dic22—21no—
22D4×Dic22C411yescharacteristic, complemented
23#10623048—22no—
24#10623048C2212yes—
25#10623001—21no—
26#10623001C2211yescharacteristic
27C2×C4×Dic22—21no—
28C2×C4×Dic22—21no—
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×#104C2211yescharacteristic
31C2×C11×#104C2211yescharacteristic
32C4×C11×M16C2211yescharacteristic
33C43×C11C2211yescharacteristic
34C2×#66901C2212yes—
35#10622731C2212yes—
36M16×Dic11C2212yes—
37C4×C4⋊Dic11—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×Dic11⋊C4—22no—
40C4×Dic11⋊C4C2212yes—
41C42×Dic11C2212yes—
42#10622537C2211yescharacteristic
43#10622314—22no—
44#10622292—21no—
45C8×Dic22—21no—
46C11×#339C2211yescharacteristic
47C11×#339C2211yescharacteristic
48#10622193C2212yes—
49#10622193C2212yes—
50#10622170C2212yes—
51#10622161C2212yes—
52#10622161C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Dic22—21no—
55C22×Dic22D411yescharacteristic
56C2×C11×M16C2311yescharacteristic
57C2×C11×M16C2311yescharacteristic
58C4×Q8×C11C2×C411yescharacteristic
59C4×Q8×C11C2×C411yescharacteristic
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11C2×C411yescharacteristic
63C4×D4×C11C2×C411yescharacteristic
64C11×#117—21no—
65C11×#117C2311yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72Q8×Dic11C2×C412yes—
73Q8×Dic11C2×C412yes—
74D4×Dic11—22no—
75D4×Dic11—22no—
76D4×Dic11C2×C412yes—
77D4×Dic11C2×C412yes—
78#66979—22no—
79#66979C2312yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83#66977—21no—
84#66977—21no—
85#66977—21no—
86#66977—21no—
87#66977—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4D412yes—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11C2312yes—
95C2×C4×Dic11C2312yes—
96C2×#4318C2312yes—
97#66943—22no—
98#66943—22no—
99#66943C2×C412yes—
100#66943C2×C412yes—
101#66941—22no—
102#66941—22no—
103#66941C2×C412yes—
104#66941C2×C412yes—
105#66931—22no—
106#66931—22no—
107#66931—22no—
108#66931—22no—
109#66931—22no—
110#66931—22no—
111#66923—22no—
112#66923C2×C412yes—
113#66922—21no—
114#66922—21no—
115#66922C2×C411yescharacteristic
116#66922C2×C411yescharacteristic
117C4×Dic22—28no—
118C4×Dic22—21no—
119C4×Dic22—21no—
120C4×Dic22—21no—
121C4×Dic22—21no—
122C4×Dic22—22no—
123C4×Dic22—22no—
124C4×Dic22—22no—
125C4×Dic22C2×C411yescharacteristic
126C4×Dic22C2×C412yes—
127C4×Dic22C2×C411yescharacteristic
128C4×Dic22D411yescharacteristic
129C4×Dic22D411yescharacteristic
130C4×Dic22D412yes—
131C11×#104—22no—
132C11×#104Q814yescomplemented
133C11×#97—21no—
134C4×C8×C11—21no—
135#66901—24no—
136C11⋊#95—21no—
137C11⋊#95—22no—
138#66879—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)—21no—
144Q8×#104—111nomaximal, Sylow
145C11×#41—21no—
146C11×#41—21no—
147C11×#41C2×Q812yes—
148C11×#41#4112yes—
149C2×Q8×C11C22×C411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C22×C411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11C2×D412yes—
164C22×Dic11C2×D412yes—
165C2×Dic22—24no—
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—44no—
171C2×Dic22C22⋊C411yescharacteristic
172C2×Dic22C22⋊C412yes—
173C2×Dic22C22⋊C411yescharacteristic
174C11×M16—21no—
175C11×M16—21no—
176C11×M16—21no—
177C11×M16C2×Q812yescomplemented
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C42×C11—24no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—42no—
195C42×C11C22×C411yescharacteristic
196C42×C11C22×C411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×Q812yescomplemented
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C22⋊Dic11—22no—
203C4⋊Dic11—24no—
204C4⋊Dic11—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11—22no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11C22⋊C411yescharacteristic
211C4⋊Dic11C22⋊C411yescharacteristic
212C4⋊Dic11C22⋊C412yes—
213C4⋊Dic11C22×C412yes—
214C4⋊Dic11C22×C412yes—
215Dic11⋊C4—28no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222Dic11⋊C4C22⋊C412yes—
223Dic11⋊C4C22⋊C412yes—
224Dic11⋊C4C22⋊C412yes—
225Dic11⋊C4C22⋊C412yes—
226C4×Dic11—28no—
227C4×Dic11—22no—
228C4×Dic11—22no—
229C4×Dic11—22no—
230C4×Dic11—22no—
231C4×Dic11—22no—
232C4×Dic11—44no—
233C4×Dic11C22×C412yes—
234C4×Dic11C22×C412yes—
235C4×Dic11C2×D412yes—
236C4×Dic11C2×D412yes—
237#4318—22no—
238#4318—22no—
239C2×C11⋊C8—22no—
240Q8×#41—111no—
241Q8×M16—111no—
242C42×Q8—111no—
243#1994—111no—
244#1994—112no—
245#1986—111no—
246#1986—112no—
247#1806—112no—
248#1806—111no—
249C4×#104—112no—
250C4×#104D1111yescharacteristic
251C23×C11—21no—
252C23×C11C22×D411yescharacteristic
253Q8×C11—21no—
254Q8×C11C4×Q812yescomplemented
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—21no—
258D4×C11C4×Q812yescomplemented
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—81no—
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C2×C22⋊C411yescharacteristic
276C2×C4×C11C2×C22⋊C411yescharacteristic
277C2×C4×C11C2×C22⋊C411yescharacteristic
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×Q811yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—44no—
292C2×Dic11—82no—
293C2×Dic11C2×C22⋊C412yes—
294C2×Dic11C2×C22⋊C412yes—
295C2×Dic11C2×C22⋊C412yes—
296C2×Dic11C2×C22⋊C412yes—
297Dic22—22no—
298Dic22—24no—
299Dic22—42no—
300Dic22—44no—
301Dic22—82no—
302Dic22—81no—
303Dic22#10414yesdirect product factor
304C8×C11—22no—
305C8×C11—41no—
306C11⋊C8—42no—
307Q82—111no—
308#557—112no—
309#557—111no—
310#554—112no—
311#554—111no—
312#554—222no—
313#554—221no—
314D4×Q8—111no—
315D4×Q8—221no—
316#533—112no—
317#533—111no—
318#533—221no—
319#533—222no—
320C4×#41—112no—
321C4×#41C2×D1111yescharacteristic
322C2×C4×Q8—111no—
323C2×C4×Q8—221no—
324C2×C4×Q8—221no—
325#446—221no—
326#446—222no—
327C8×Q8—221no—
328#423—112no—
329#423—111no—
330C2×#104—112no—
331C2×#104C2×D1111yescharacteristic
332C2×#104C2×D1111yescharacteristic
333C4×M16—112no—
334C4×M16C2×D1111yescharacteristic
335C4×C4⋊C4—112no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—222no—
338C4×C4⋊C4—221no—
339C43—112no—
340C43C2×D1111yescharacteristic
341#339—112no—
342#339—112no—
343#339—112no—
344#339—112no—
345#339—112no—
346#339C2×D1111yescharacteristic
347#339C2×D1111yescharacteristic
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11C22×C22⋊C411yescharacteristic
354C22×C11#54811yescharacteristic
355C22×C11D4×Q811yescharacteristic
356C4×C11—24no—
357C4×C11—22no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11C2×#10412yes—
365C4×C11C2×C4×Q811yescharacteristic
366C4×C11#51911yescharacteristic
367C4×C11#54811yescharacteristic
368C4×C11D4×Q811yescharacteristic
369Dic11—22no—
370Dic11—22no—
371Dic11—22no—
372Dic11—44no—
373Dic11—42no—
374Dic11—42no—
375Dic11C2×#10414yes—
376C2×#41C22×D1111yescharacteristic
377C22×Q8—111no—
378C22×Q8—221no—
379C2×M16—112no—
380C2×M16C22×D1111yescharacteristic
381C2×M16C22×D1111yescharacteristic
382C4⋊Q8—112no—
383C4⋊Q8—112no—
384C4⋊Q8—111no—
385C4⋊Q8—111no—
386C4⋊Q8—221no—
387C4⋊Q8—221no—
388C4⋊Q8—222no—
389C4⋊Q8—222no—
390#125—112no—
391#125—112no—
392#125—112no—
393#125—222no—
394#125—222no—
395#125—222no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401C22⋊Q8—222no—
402C22⋊Q8—221no—
403C22⋊Q8—222no—
404C22⋊Q8—221no—
405C22⋊Q8—221no—
406C22⋊Q8—221no—
407C4×Q8—111no—
408C4×Q8—111no—
409C4×Q8—112no—
410C4×Q8—111no—
411C4×Q8—112no—
412C4×Q8—111no—
413C4×Q8—112no—
414C4×Q8—112no—
415C4×Q8—222no—
416C4×Q8—222no—
417C4×Q8—222no—
418C4×Q8—221no—
419C4×Q8—221no—
420C4×Q8—228no—
421C4×Q8—221no—
422C4×Q8—221no—
423C4×Q8C4×D1111yescharacteristic
424C4×Q8C4×D1111yescharacteristic
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—112no—
428C4×D4—112no—
429C4×D4—222no—
430C4×D4—222no—
431C4×D4C4×D1111yescharacteristic
432C4×D4C4×D1111yescharacteristic
433#117—21no—
434#117—112no—
435#117—222no—
436#117C22×D1111yescharacteristic
437C2×C4⋊C4—112no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—221no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—112no—
447C2×C42—112no—
448C2×C42—222no—
449C2×C42—222no—
450C2×C42—222no—
451C2×C42C22×D1111yescharacteristic
452C2×C42C22×D1111yescharacteristic
453C2×C42C22×D1111yescharacteristic
454C4⋊C8—222no—
455C4⋊C8—222no—
456C4⋊C8—221no—
457C4⋊C8—221no—
458#104—22no—
459#104—224no—
460#104Dic2214yesdirect product factor
461#97—21no—
462#97—222no—
463C4×C8—21no—
464C4×C8—222no—
465#95—222no—
466#95—221no—
467C2×C11—21no—
468C2×C11—21no—
469C2×C11—42no—
470C2×C11Q8×C22⋊C411yescharacteristic
471C2×C11C22×#10411yescharacteristic
472C2×C11#290111yescharacteristic
473#41—21no—
474#41—21no—
475#41C2×Dic2212yes—
476#41#433912yes—
477C2×Q8—111no—
478C2×Q8—112no—
479C2×Q8—111no—
480C2×Q8—222no—
481C2×Q8—222no—
482C2×Q8—224no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—444no—
486C2×Q8C2×C4×D1111yescharacteristic
487C2×D4—21no—
488C2×D4C2×C4×D1111yescharacteristic
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502M16—21no—
503M16—21no—
504M16—21no—
505M16—222no—
506M16—222no—
507M16C2×Dic2212yescomplemented
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—222no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—112no—
514C4⋊C4—111no—
515C4⋊C4—112no—
516C4⋊C4—112no—
517C4⋊C4—112no—
518C4⋊C4—112no—
519C4⋊C4—111no—
520C4⋊C4—112no—
521C4⋊C4—112no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4—228no—
531C4⋊C4—224no—
532C4⋊C4—222no—
533C4⋊C4—221no—
534C4⋊C4—222no—
535C4⋊C4—221no—
536C4⋊C4C2×C4×D1111yescharacteristic
537C4⋊C4C2×C4×D1111yescharacteristic
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—222no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C42—24no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—112no—
553C42—112no—
554C42—112no—
555C42—112no—
556C42—222no—
557C42—222no—
558C42—228no—
559C42—222no—
560C42—222no—
561C42—222no—
562C42—444no—
563C42C2×Dic2212yescomplemented
564C42C2×C4×D1111yescharacteristic
565C42C2×C4×D1111yescharacteristic
566C42D4×D1111yescharacteristic
567C42D4×D1111yescharacteristic
568C11Q8×#10411yescharacteristic, complemented, Sylow
569C23—21no—
570C23C2×D4×D1111yescharacteristic
571Q8—21no—
572Q8—114no—
573Q8—224no—
574Q8—222no—
575Q8—444no—
576Q8—442no—
577Q8—881no—
578Q8—882no—
579Q8C4×Dic2212yescomplemented
580D4—22no—
581D4—22no—
582D4—21no—
583D4C4×Dic2212yescomplemented
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—81no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—444no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—882no—
612C2×C4C22⋊C4×D1111yescharacteristic
613C2×C4C22⋊C4×D1111yescharacteristic
614C2×C4C22⋊C4×D1111yescharacteristic
615C2×C4C22⋊C4×D1111yescharacteristic
616C2×C4C22×Dic2211yescharacteristic
617C2×C4C22×C4×D1111yescharacteristic
618C2×C4C2×#433911yescharacteristic
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4#6704311yescharacteristic
621C2×C4#6704311yescharacteristic
622C8—22no—
623C8—41no—
624C8—442no—
625C22—21no—
626C22—21no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22C2×C22⋊C4×D1111yescharacteristic
631C22D4×Dic2211yescharacteristic
632C22#1062308311yescharacteristic
633C4—24no—
634C4—22no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—114no—
642C4—222no—
643C4—222no—
644C4—222no—
645C4—444no—
646C4—442no—
647C4—442no—
648C4D11×#10412yes—
649C4C2×C4×Dic2211yescharacteristic
650C4#1062304711yescharacteristic
651C4D4×Dic2211yescharacteristic
652C4#1062308311yescharacteristic
653C2—21no—
654C2—21no—
655C2—42no—
656C2C22⋊C4×Dic2211yescharacteristic
657C2C2×D11×#10411yescharacteristic
658C2#1307716011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#104C2
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenterC4×#104D11
hypocenterC11Q8×#104
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. M16×Dic22C2semidirect
3. C42×Dic22C2semidirect
4. #13069593C2semidirect
5. #13069591C2semidirect
6. #13069560C2semidirect
7. #13069558C2semidirect
14. #10623101C4semidirect
15. #10623100C4semidirect
16. Q8×Dic22C4semidirect
18. #10623074C4semidirect
20. #10623070C4semidirect
22. D4×Dic22C4semidirect
132. C11×#104Q8semidirect
177. C11×M16C2×Q8semidirect
199. C42×C11C2×Q8semidirect
254. Q8×C11C4×Q8semidirect
258. D4×C11C4×Q8semidirect
303. Dic22#104direct (N × H)
460. #104Dic22direct (N × H)
507. M16C2×Dic22semidirect
563. C42C2×Dic22semidirect
568. C11Q8×#104semidirect
579. Q8C4×Dic22semidirect
583. D4C4×Dic22semidirect

Maximal subgroups

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

subgroupindex
#41×Dic222
M16×Dic222
C42×Dic222
#130695932
#130695912
#130695602
#130695582
#130686362
#130686342
#104×Dic112
C4×C11×#1042
Q8×#10411