Finite Group Databasebeta

← #14788897

Subgroups — #14788897

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic
2C2×#10622641C212yesmaximal, complemented
3C2×#10622663C211yesmaximal, characteristic, complemented
4C2×#10622659C211yesmaximal, characteristic
5#13069857C212yesmaximal, complemented
6#13069709C212yesmaximal, complemented
7#13069548C212yesmaximal, complemented
8#13068596C211yesmaximal, characteristic, complemented
9#13068550C211yesmaximal, characteristic, complemented
10#13068546C211yesmaximal, characteristic
11C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C22×#4326C2212yescomplemented
18C22×#4325C2212yes—
19C22×(C2×D11)⋊C4—21no—
20C22×(C2×D11)⋊C4—21no—
21C2×#66928—21no—
22C2×#66928—21no—
23C2×#66928—28no—
24C2×#66928C2212yes—
25C2×#66928C2212yes—
26C11×#391C2211yescharacteristic, complemented
27C11×#389C2211yescharacteristic, complemented
28C11×#387—21no—
29C11×#385—21no—
30C11×#380C2211yescharacteristic
31C4×C11×C4⋊C4—21no—
32C4×C11×C4⋊C4C2211yescharacteristic, complemented
33C4×C11×C22⋊C4—21no—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622663—24no—
37#10622659—24no—
38#10622641—28no—
39C2×#66874C2212yescomplemented
40C2×#66874C2212yescomplemented
41C2×#66874C2212yescomplemented
42C2×#66873C2212yes—
43C2×#66873C2212yes—
44C2×#66873C2212yes—
45C2×C4⋊(C11⋊C8)C2212yescomplemented
46#10622162C2212yescomplemented
47C24×D11—21no—
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—21no—
53C22×D44—21no—
54C22×D44—24no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—42no—
58C22×D44C2312yes—
59C22×Dic22—21no—
60C22×Dic22—24no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—42no—
64C22×Dic22C2312yes—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8D414yes—
67C4×Q8×C11—24no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—24no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11D411yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×#4326—24no—
84C2×#4326—24no—
85C2×#4326—42no—
86C2×#4325—24no—
87C2×#4325—24no—
88C2×#4325—42no—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2312yes—
97#66928—28no—
98#66928—28no—
99#66928—24no—
100#66928—24no—
101#66928—24no—
102#66928D418yes—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—22no—
110#66874—24no—
111#66874—24no—
112#66874—42no—
113#66873—24no—
114#66873—24no—
115#66873—42no—
116C4⋊(C11⋊C8)—24no—
117#24217—111nomaximal, Sylow
118C24×C11C2×D411yescharacteristic
119C23×D11—24no—
120C23×D11—22no—
121C23×D11—42no—
122C23×D11—42no—
123C23×D11—42no—
124C23×D11—42no—
125C23×D11—42no—
126C23×D11—42no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11C2×D412yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C2×D44—24no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—48no—
162C2×D44—48no—
163C2×D44—42no—
164C2×D44—42no—
165C2×D44C2×D414yes—
166C2×Dic22—24no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—48no—
173C2×Dic22—48no—
174C2×Dic22—42no—
175C2×Dic22—42no—
176C2×Dic22C2×D414yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4C2×D412yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—42no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—42no—
190C42×C11—42no—
191C42×C11C2×D414yes—
192#4326—48no—
193#4325—48no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—28no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C22×#124—111no—
205C2×#464—112no—
206C2×#451—111no—
207C2×#450—111no—
208C4×C22⋊Q8D1111yescharacteristic, complemented
209#2042—112no—
210#2015—112no—
211#1983—112no—
212#1797—111no—
213#1787—111no—
214#1786—111no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11#12112yes—
220C23×C11#13512yes—
221C23×C11#13712yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—24no—
224C22×D11—48no—
225C22×D11—48no—
226C22×D11—48no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—84no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11—84no—
237Q8×C11—24no—
238Q8×C11—42no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11#12012yes—
268C2×C4×C11#12012yes—
269C2×C4×C11#12112yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D412yes—
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)12yes—
274C2×Dic11—24no—
275C2×Dic11—48no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278D44—24no—
279D44—24no—
280D44—48no—
281D44—42no—
282D44—42no—
283Dic22—24no—
284Dic22—24no—
285Dic22—48no—
286Dic22—42no—
287Dic22—42no—
288C11⋊C8—42no—
289C11⋊C8—42no—
290C23×Q8—111no—
291C23×D4—111no—
292C22×Q16—112no—
293C22×SD16—112no—
294C2×#124—112no—
295C2×#124—112no—
296C2×#124—228no—
297C2×#124—221no—
298C2×#124—221no—
299C2×C22⋊Q8C2×D1111yescharacteristic
300C2×C4×Q8C2×D1111yescharacteristic, complemented
301C22×C22⋊C4—221no—
302C22×C22⋊C4—221no—
303C22×C42C2×D1111yescharacteristic
304#464—228no—
305#451—224no—
306#450—224no—
307C2×C4⋊C8—112no—
308C2×#103—112no—
309C2×#103—112no—
310C2×#103—112no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316#391C2×D1111yescharacteristic, complemented
317#389C2×D1111yescharacteristic, complemented
318#387—21no—
319#385—21no—
320#380C2×D1111yescharacteristic
321C4×C4⋊C4—21no—
322C4×C4⋊C4C2×D1111yescharacteristic, complemented
323C4×C22⋊C4—21no—
324#336—112no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11#46414yescomplemented
332C22×C11C2×#12011yescharacteristic
333C22×C11C2×#12111yescharacteristic
334C22×C11#53511yescharacteristic
335C22×C11C2×#13511yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57511yescharacteristic
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—816no—
343C2×D11—82no—
344C2×D11—82no—
345C2×D11—82no—
346C2×D11—82no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11D4212yes—
357C4×C11#54612yes—
358Dic11—44no—
359C25—221no—
360C22×Q8—112no—
361C22×Q8—224no—
362C22×Q8—221no—
363C22×Q8—222no—
364C22×Q8—222no—
365C22×Q8—442no—
366C22×Q8C22×D1111yescharacteristic
367C22×D4—112no—
368C22×D4—224no—
369C22×D4—222no—
370C22×D4—222no—
371C22×D4—221no—
372C22×D4—442no—
373C23×C4—221no—
374C23×C4C22⋊D1111yescharacteristic
375C23×C4C22⋊D1111yescharacteristic
376C23×C4C22×D1111yescharacteristic
377C2×Q16—224no—
378C2×Q16—224no—
379C2×Q16—442no—
380C2×SD16—224no—
381C2×SD16—224no—
382C2×SD16—442no—
383C22×C8—112no—
384C22×C8—112no—
385#124—118no—
386#124—224no—
387#124—224no—
388#124—228no—
389#124—228no—
390#124—224no—
391C22⋊Q8—22no—
392C22⋊Q8D4414yes—
393C4×Q8—24no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—228no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—222no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4—222no—
408C2×C42—24no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C22⋊D1111yescharacteristic
412C2×C42C22⋊D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415C4⋊C8—224no—
416#103—224no—
417#103—224no—
418#103—442no—
419#102—224no—
420#102—224no—
421#102—442no—
422C22⋊C8—222no—
423C22⋊C8—222no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429C2×C11—24no—
430C2×C11#240811yescharacteristic
431C2×C11#300211yescharacteristic
432C2×C11#300711yescharacteristic
433C2×C11C2×#46411yescharacteristic
434C2×C11#304011yescharacteristic
435C2×C11#321111yescharacteristic
436C2×C11#321511yescharacteristic
437D11—84no—
438C24—224no—
439C24—222no—
440C24—442no—
441C24—442no—
442C24—442no—
443C24—442no—
444C24—442no—
445C24—442no—
446C24C2×C22⋊D1111yescharacteristic
447C2×Q8—21no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—114no—
451C2×Q8—224no—
452C2×Q8—222no—
453C2×Q8—222no—
454C2×Q8—222no—
455C2×Q8—222no—
456C2×Q8—222no—
457C2×Q8—448no—
458C2×Q8—448no—
459C2×Q8—442no—
460C2×Q8—442no—
461C2×Q8C2×D4412yes—
462C2×D4—114no—
463C2×D4—224no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—222no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—448no—
470C2×D4—448no—
471C2×D4—442no—
472C2×D4—442no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—224no—
486C22×C4—222no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4C2×D4412yes—
490C22×C4#433912yes—
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497Q16—448no—
498SD16—448no—
499C2×C8—222no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—222no—
504C2×C8—222no—
505C4⋊C4—24no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4C2×D4412yes—
512C22⋊C4—24no—
513C22⋊C4—42no—
514C22⋊C4—228no—
515C22⋊C4—228no—
516C22⋊C4—228no—
517C22⋊C4—228no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—42no—
522C42—42no—
523C42D4×D1114yes—
524C11#2421711yescharacteristic, complemented, Sylow
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—224no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—884no—
540C23—884no—
541C23—884no—
542C23—884no—
543C23#6698312yes—
544C23#6699512yes—
545C23#6700312yes—
546C23C22×C22⋊D1111yescharacteristic
547Q8—24no—
548Q8—42no—
549Q8—224no—
550Q8—224no—
551Q8—448no—
552Q8—442no—
553Q8—442no—
554D4—224no—
555D4—224no—
556D4—448no—
557D4—442no—
558D4—442no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—224no—
588C2×C4—448no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4#6698312yes—
592C2×C4#6699012yes—
593C2×C4#6699012yes—
594C2×C4C22×D4411yescharacteristic
595C2×C4C2×#433911yescharacteristic
596C2×C4C2×D4×D1112yes—
597C2×C4#6704212yes—
598C8—442no—
599C8—442no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—444no—
607C22—444no—
608C22—444no—
609C22—8816no—
610C22—882no—
611C22—882no—
612C22—882no—
613C22—882no—
614C22#1062264114yescomplemented
615C22C2×#6698311yescharacteristic
616C22C2×#6699011yescharacteristic
617C22C2×#6699511yescharacteristic
618C22C2×#6700311yescharacteristic
619C22#1062335311yescharacteristic
620C22#1062335311yescharacteristic
621C22#1062336111yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—444no—
632C4D4×D4412yes—
633C4#1062308112yes—
634C2—24no—
635C2—884no—
636C2#1307197211yescharacteristic
637C2#1307783211yescharacteristic
638C2#1307787411yescharacteristic
639C2C2×#1062264111yescharacteristic
640C2#1307811011yescharacteristic
641C2#1307957711yescharacteristic
642C2#1307961511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenterC4×C22⋊Q8D11
hypocenterC11#24217
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622641C2semidirect
3. C2×#10622663C2semidirect
5. #13069857C2semidirect
6. #13069709C2semidirect
7. #13069548C2semidirect
8. #13068596C2semidirect
9. #13068550C2semidirect
11. C4×C11×C22⋊Q8C2semidirect
15. C2×C4×Q8×C11C22semidirect
17. C22×#4326C22semidirect
26. C11×#391C22semidirect
27. C11×#389C22semidirect
32. C4×C11×C4⋊C4C22semidirect
39. C2×#66874C22semidirect
40. C2×#66874C22semidirect
41. C2×#66874C22semidirect
45. C2×C4⋊(C11⋊C8)C22semidirect
46. #10622162C22semidirect
208. C4×C22⋊Q8D11semidirect
300. C2×C4×Q8C2×D11semidirect
316. #391C2×D11semidirect
317. #389C2×D11semidirect
322. C4×C4⋊C4C2×D11semidirect
331. C22×C11#464semidirect
524. C11#24217semidirect
614. C22#10622641semidirect

Maximal subgroups

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

subgroupindex
C22×#669282
C2×#106226412
C2×#106226632
C2×#106226592
#130698572
#130697092
#130695482
#130685962
#130685502
#130685462
C4×C11×C22⋊Q82
#2421711