Finite Group Databasebeta

← #14780622

Subgroups — #14780622

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×#66995C211yesmaximal, characteristic, complemented
2C2×#10623322C211yesmaximal, characteristic
3C2×#10622579C211yesmaximal, characteristic, complemented
4C2×#10622838C211yesmaximal, characteristic, complemented
5C2×#10622820C211yesmaximal, characteristic, complemented
6#13069624C214yesmaximal, complemented
7#13069617C214yesmaximal, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×#4339C2211yescharacteristic
13C2×C11×C22⋊Q8—24no—
14C2×C11×C22⋊Q8—22no—
15C2×C11×C22⋊Q8—24no—
16C2×C11×C22⋊Q8C2214yes—
17C22×C11×C4⋊C4—21no—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C2×#67006—21no—
21C22×#4326C2212yescomplemented
22C2×#66995—24no—
23C2×#66995—24no—
24C2×#66995—24no—
25C22×#4325C2212yescomplemented
26#10623322—24no—
27#10623322—24no—
28C2×#66983C2212yes—
29C2×#66982—21no—
30C2×C4×C22⋊D11—22no—
31C2×#66979C2211yescharacteristic
32C2×#66977C2212yes—
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35#10622838—24no—
36C2×#66899C2214yescomplemented
37#10622820—24no—
38C2×C22⋊(C11⋊C8)C2214yes—
39C2×#66874C2212yescomplemented
40#10622579—24no—
41C2×#66873C2212yescomplemented
42#10622167C2214yescomplemented
43C25×C11D411yescharacteristic
44C22×Q8×C11—22no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11D414yescomplemented
51C22×Q8×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11D412yes—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C22×C22⋊D11—21no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339D414yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×Dic22C2311yescharacteristic
75C11×C22⋊Q8—216no—
76C11×C22⋊Q8—28no—
77C11×C22⋊Q8—28no—
78C2×C11×C4⋊C4—28no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4D414yescomplemented
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4—24no—
86#67006—28no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—21no—
89C2×#4326—24no—
90C2×#4326—24no—
91C2×#4326—24no—
92#66995—232no—
93C2×#4325—24no—
94C2×#4325—24no—
95C2×#4325—24no—
96#66983—24no—
97#66983—24no—
98#66982—28no—
99C4×C22⋊D11—216no—
100C2×(C2×D11)⋊C4—22no—
101#66979—22no—
102#66979D414yes—
103C2×C4⋊Dic11C2312yes—
104#66977—24no—
105#66977—24no—
106C2×Dic11⋊C4—22no—
107C2×C4×Dic11—21no—
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—28no—
117C22⋊(C11⋊C8)—28no—
118#66874—24no—
119#66873—24no—
120#23392—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11—24no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—42no—
126C24×C11C2×D412yes—
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—28no—
132C2×Q8×C11—28no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—42no—
138C2×Q8×C11—42no—
139C2×Q8×C11—44no—
140C2×Q8×C11—44no—
141C2×Q8×C11C2×D414yes—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—44no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—44no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11—44no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11#4112yes—
173C22×C4×C11C2411yescharacteristic
174C2×C22⋊D11—28no—
175C2×C22⋊D11—24no—
176C2×C22⋊D11—44no—
177C2×C22⋊D11—42no—
178C2×C22⋊D11—42no—
179C2×C22⋊D11—44no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182#4339—28no—
183#4339—28no—
184#4339—44no—
185#4339—44no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44C2×D412yes—
192C2×C4×D11—24no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22C2×D412yes—
201C11×C4⋊C4—216no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4C2×D414yes—
205C11×C22⋊C4—216no—
206C22⋊Dic11—28no—
207C22⋊Dic11—24no—
208#4326—216no—
209#4325—216no—
210(C2×D11)⋊C4—28no—
211C4⋊Dic11—22no—
212C4⋊Dic11C2×D414yes—
213Dic11⋊C4—28no—
214C4×Dic11—24no—
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×#525—111no—
225C22×C22⋊Q8D1111yescharacteristic, complemented
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—48no—
242C23×C11—48no—
243C23×C11—44no—
244C23×C11—44no—
245C23×C11#12012yes—
246C23×C11#12012yes—
247C23×C11#12112yes—
248C23×C11#13714yescomplemented
249C23×C11C22×D411yescharacteristic
250C22×D11—22no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—42no—
254C22×D11—42no—
255Q8×C11—24no—
256Q8×C11—24no—
257Q8×C11—42no—
258Q8×C11—42no—
259Q8×C11—48no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—48no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—44no—
269C2×C4×C11—44no—
270C2×C4×C11—48no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—48no—
276C2×C4×C11#12014yes—
277C2×C4×C11#12012yes—
278C2×C4×C11#12012yes—
279C2×C4×C11#12114yes—
280C2×C4×C11#12114yes—
281C2×C4×C11#12112yes—
282C2×C4×C11#12714yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C22⋊D11—416no—
290C22⋊D11—48no—
291C2×Dic11—24no—
292C2×Dic11—22no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297D44—22no—
298D44—22no—
299D44—41no—
300D44—41no—
301C4×D11—48no—
302Dic22—22no—
303Dic22—22no—
304Dic22—41no—
305Dic22—41no—
306C11⋊C8—24no—
307C11⋊C8—42no—
308C22×#41—111no—
309C23×Q8C2×D1111yescharacteristic
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—224no—
319#525—224no—
320C2×#123—221no—
321C2×C22⋊Q8—24no—
322C2×C22⋊Q8—22no—
323C2×C22⋊Q8—24no—
324C2×C22⋊Q8—112no—
325C2×C22⋊Q8C2×D1114yes—
326C2×#121—112no—
327C2×#120—221no—
328C2×C4×D4—222no—
329C2×#117—111no—
330C22×C4⋊C4—21no—
331C22×C4⋊C4C2×D1111yescharacteristic
332C22×C22⋊C4—21no—
333#419—224no—
334#417—224no—
335C2×#103—114no—
336C2×#103—112no—
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#39214yes—
354C22×C11C2×#12011yescharacteristic
355C22×C11C2×#12011yescharacteristic
356C22×C11C2×#12111yescharacteristic
357C22×C11C2×#13712yes—
358C22×C11#57512yes—
359C2×D11—42no—
360C2×D11—44no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—82no—
364C4×C11—42no—
365C4×C11—44no—
366C4×C11—44no—
367C4×C11#39214yes—
368C4×C11C2×#12011yescharacteristic
369C4×C11C2×#12111yescharacteristic
370C4×C11C2×#12111yescharacteristic
371C4×C11C2×#12711yescharacteristic
372Dic11—42no—
373Dic11—44no—
374C25C22⋊D1111yescharacteristic
375C2×#41—114no—
376C2×#41—222no—
377C2×#41—222no—
378C2×#41—222no—
379C2×#41—222no—
380C2×#41—222no—
381C22×Q8—22no—
382C22×Q8—21no—
383C22×Q8—22no—
384C22×Q8—22no—
385C22×Q8—22no—
386C22×Q8—22no—
387C22×Q8—111no—
388C22×Q8C22⋊D1114yescomplemented
389C22×Q8C22×D1112yes—
390C22×D4—111no—
391C22×D4—222no—
392C22×D4—221no—
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
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—228no—
422C22⋊Q8—216no—
423C22⋊Q8—28no—
424C22⋊Q8—28no—
425C22⋊Q8—224no—
426C22⋊Q8—224no—
427#121—224no—
428#121—224no—
429#120—228no—
430C4×D4—2216no—
431#117—114no—
432#117—222no—
433C2×C4⋊C4—28no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—222no—
439C2×C4⋊C4C22⋊D1114yescomplemented
440C2×C4⋊C4C22×D1112yes—
441C2×C22⋊C4—28no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—222no—
445C2×C22⋊C4—222no—
446C2×C42—221no—
447#103—228no—
448#103—224no—
449#102—224no—
450C22⋊C8—228no—
451C2×C11—24no—
452C2×C11—44no—
453C2×C11C2×#39211yescharacteristic
454C2×C11#300411yescharacteristic
455C2×C11#300511yescharacteristic
456C2×C11#300712yes—
457C2×C11#305612yes—
458D11—82no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—42no—
464C24—221no—
465C24C2×C22⋊D1112yes—
466C24C2×C22⋊D1111yescharacteristic
467#41—228no—
468#41—228no—
469#41—444no—
470#41—444no—
471C2×Q8—24no—
472C2×Q8—22no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—42no—
482C2×Q8—44no—
483C2×Q8—112no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8C2×C22⋊D1114yes—
490C2×D4—112no—
491C2×D4—228no—
492C2×D4—224no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—444no—
499C2×D4—442no—
500C2×D4—444no—
501C2×D4—442no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—44no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—222no—
526C22×C4—221no—
527C22×C4—224no—
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—216no—
550C4⋊C4—24no—
551C4⋊C4—22no—
552C4⋊C4—114no—
553C4⋊C4—228no—
554C4⋊C4—222no—
555C4⋊C4C2×C22⋊D1114yes—
556C22⋊C4—216no—
557C22⋊C4—228no—
558C22⋊C4—228no—
559C22⋊C4—224no—
560C42—224no—
561C11#2339211yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—28no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—48no—
572C23—48no—
573C23—44no—
574C23—44no—
575C23—222no—
576C23—441no—
577C23—442no—
578C23—442no—
579C23—441no—
580C23#6699012yes—
581C23#6699212yes—
582C23#6699514yescomplemented
583C23#6700612yes—
584C23C22×C22⋊D1111yescharacteristic
585Q8—24no—
586Q8—24no—
587Q8—42no—
588Q8—42no—
589Q8—48no—
590Q8—222no—
591Q8—222no—
592Q8—441no—
593Q8—441no—
594D4—222no—
595D4—222no—
596D4—4416no—
597D4—448no—
598D4—441no—
599D4—441no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—48no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—48no—
610C2×C4—44no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—48no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—441no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—441no—
622C2×C4—448no—
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—444no—
651C22—442no—
652C22—881no—
653C22—881no—
654C22—882no—
655C22#1062283614yes—
656C22C2×#6699011yescharacteristic
657C22C2×#6699211yescharacteristic
658C22C2×#6699512yes—
659C22#1062335312yes—
660C22C2×#6700611yescharacteristic
661C4—44no—
662C4—42no—
663C4—44no—
664C4—444no—
665C4—442no—
666C4#1062283614yes—
667C4C2×#6699011yescharacteristic
668C4C2×#6699111yescharacteristic
669C4C2×#6699211yescharacteristic
670C4C2×#6699311yescharacteristic
671C2—24no—
672C2—44no—
673C2—882no—
674C2C2×#1062283611yescharacteristic
675C2#1307785011yescharacteristic
676C2#1307785811yescharacteristic
677C2#1307787412yes—
678C2#1307824212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
hypercenterC22×C22⋊Q8D11
hypocenterC11#23392
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
3. C2×#10622579C2semidirect
4. C2×#10622838C2semidirect
5. C2×#10622820C2semidirect
6. #13069624C2semidirect
7. #13069617C2semidirect
8. #13068335C2semidirect
9. C22×C11×C22⋊Q8C2semidirect
21. C22×#4326C22semidirect
25. C22×#4325C22semidirect
36. C2×#66899C22semidirect
39. C2×#66874C22semidirect
41. C2×#66873C22semidirect
42. #10622167C22semidirect
50. C22×Q8×C11D4semidirect
82. C2×C11×C4⋊C4D4semidirect
113. C2×#4318D4semidirect
225. C22×C22⋊Q8D11semidirect
248. C23×C11#137semidirect
388. C22×Q8C22⋊D11semidirect
439. C2×C4⋊C4C22⋊D11semidirect
561. C11#23392semidirect
582. C23#66995semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106233222
C2×#106225792
C2×#106228382
C2×#106228202
#130696242
#130696172
#130683352
C22×C11×C22⋊Q82
#2339211