Finite Group Databasebeta

← #14782467

Subgroups — #14782467

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×#10622734C211yesmaximal, characteristic, complemented
2C2×#10622746C211yesmaximal, characteristic
3C2×#10622746C211yesmaximal, characteristic
4#13071106C211yesmaximal, characteristic
5C2×#10622541C211yesmaximal, characteristic, complemented
6#13070010C212yesmaximal, complemented
7#13070003C212yesmaximal, complemented
8#13069996C212yesmaximal, complemented
9#13069989C212yesmaximal, complemented
10#13068336C211yesmaximal, characteristic, complemented
11C2×C11×#423C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4—21no—
20C11×#423—24no—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C4⋊C8C2212yes—
23#10622826—21no—
24#10622826—21no—
25C2×C11⋊#95—21no—
26#10622746—24no—
27#10622746—24no—
28#10622734—24no—
29C2×#66885C2212yes—
30C2×#66885C2212yes—
31C2×#66882C2212yes—
32C2×#66881C2212yes—
33C2×#66880C2212yes—
34C2×#66880C2212yes—
35#10622552C2211yescharacteristic
36#10622552C2211yescharacteristic
37C4×(C2×D11)⋊C4—21no—
38C4×(C2×D11)⋊C4—21no—
39#10622542C2211yescharacteristic
40#10622542C2211yescharacteristic
41#10622541—21no—
42#10622541—21no—
43#10622541C2212yes—
44#10622541C2212yes—
45#10622189C2212yes—
46#10622189C2212yes—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C23×Dic11—21no—
52C23×Dic11—21no—
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—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16D414yes—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11D411yescharacteristic
73C2×C42×C11D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81#66979—22no—
82#66979—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11D414yes—
89C2×C4⋊Dic11C2312yes—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2312yes—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—44no—
96C2×C4×Dic11—21no—
97C11×C4⋊C8—24no—
98C11×C4⋊C8—24no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105#66885—24no—
106#66885—24no—
107#66882—24no—
108#66881—24no—
109#66880—24no—
110#66880—24no—
111#23617—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×Q812yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—24no—
133C2×C22⋊D11—42no—
134C2×C22⋊D11—42no—
135C22×Dic11—24no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—22no—
141C22×Dic11—42no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
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—28no—
166C11×M16—44no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2×D414yes—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C22⋊Dic11—42no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184C4⋊Dic11—24no—
185C4⋊Dic11—22no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—22no—
189C4⋊Dic11—22no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11C2×D414yes—
194Dic11⋊C4—44no—
195Dic11⋊C4—44no—
196C4×Dic11—42no—
197C2×#428—111no—
198C2×#423D1111yescharacteristic, complemented
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#1736—111no—
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—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11#12112yes—
236C2×C4×C11#12112yes—
237C2×C4×C11#12114yes—
238C2×C4×C11C22⋊Q814yes—
239C2×C4×C11C22⋊Q812yes—
240C2×C4×C11C22⋊Q814yes—
241C2×C4×C11#12614yes—
242C2×C4×C11AGL(1,ℤ/8)12yes—
243C2×C4×C11#13712yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—48no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—48no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—42no—
267C2×Dic11—84no—
268D44—22no—
269D44—22no—
270D44—41no—
271D44—41no—
272C4×D11—48no—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—24no—
278C8×C11—42no—
279C22×#41—111no—
280C22×M16C2×D1111yescharacteristic
281C22×M16C2×D1111yescharacteristic
282C2×#117—111no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—221no—
286C22×C42C2×D1111yescharacteristic
287#428—224no—
288C2×#107—112no—
289C2×#106—112no—
290#423—24no—
291C2×C4⋊C8C2×D1112yes—
292C2×C4⋊C8C2×D1112yes—
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#340—112no—
313#340—112no—
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—22no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11#39614yes—
340C4×C11C2×#12111yescharacteristic
341C4×C11C2×C22⋊Q811yescharacteristic
342C4×C11C2×C22⋊Q811yescharacteristic
343C4×C11C2×#12611yescharacteristic
344Dic11—42no—
345Dic11—44no—
346Dic11—81no—
347Dic11—81no—
348Dic11—82no—
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—221no—
359C23×C4—221no—
360C23×C4—221no—
361C23×C4D4411yescharacteristic
362C23×C4D4411yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16C22⋊D1114yes—
370C22×C8C22×D1112yes—
371C22×C8C22×D1112yes—
372#117—222no—
373#117—222no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—444no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—221no—
395C2×C42D4411yescharacteristic
396C2×C42D4411yescharacteristic
397C2×C42C22×D1111yescharacteristic
398C2×C42C22×D1111yescharacteristic
399#107—224no—
400#106—224no—
401C4⋊C8—24no—
402C4⋊C8—24no—
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—
423C24C2×D4411yescharacteristic
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—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—224no—
450C22×C4—221no—
451C22×C4—222no—
452C22×C4—224no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4C2×D4411yescharacteristic
464C22×C4C2×D4411yescharacteristic
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4#433912yes—
469C22×C4D4×D1112yes—
470C22×C4#434112yes—
471C22×C4Q8×D1112yes—
472C22×C4#434312yes—
473C22×C4C2×C22⋊D1112yes—
474C22×C4C23×D1111yescharacteristic
475M16—28no—
476M16—44no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8C2×C22⋊D1114yes—
483C4⋊C4—114no—
484C4⋊C4—224no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—222no—
492C4⋊C4—444no—
493C4⋊C4—444no—
494C4⋊C4—442no—
495C22⋊C4—442no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—22no—
501C42—22no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—442no—
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#6694812yes—
520C23#6695012yes—
521C23#6698312yes—
522C23C22×D4411yescharacteristic
523Q8—222no—
524Q8—222no—
525Q8—441no—
526Q8—441no—
527D4—222no—
528D4—222no—
529D4—448no—
530D4—441no—
531D4—441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—448no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—448no—
552C2×C4—441no—
553C2×C4—442no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—442no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—442no—
561C2×C4—884no—
562C2×C4#6694812yes—
563C2×C4#6694914yes—
564C2×C4#6695012yes—
565C2×C4#6695114yes—
566C2×C4#6696112yes—
567C2×C4#6696212yes—
568C2×C4#6698312yes—
569C2×C4#6699214yes—
570C2×C4#6699914yes—
571C2×C4C2×#433911yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×#434111yescharacteristic
574C2×C4C2×Q8×D1111yescharacteristic
575C2×C4C2×#434311yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—24no—
578C8—42no—
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#1062260714yes—
593C22C2×#6694811yescharacteristic
594C22C2×#6695011yescharacteristic
595C22C2×#6696111yescharacteristic
596C22C2×#6696211yescharacteristic
597C22#1062327911yescharacteristic
598C22#1062327911yescharacteristic
599C22C2×#6698311yescharacteristic
600C4—22no—
601C4—22no—
602C4—41no—
603C4—41no—
604C4—444no—
605C4—442no—
606C4—881no—
607C4—881no—
608C4—882no—
609C4#1062260714yes—
610C4C2×#6694911yescharacteristic
611C4C2×#6695111yescharacteristic
612C4C2×#6699211yescharacteristic
613C4C2×#6699911yescharacteristic
614C2—24no—
615C2—882no—
616C2C2×#1062260711yescharacteristic
617C2#1307808211yescharacteristic
618C2#1307809011yescharacteristic
619C2#1307823511yescharacteristic
620C2#1307824611yescharacteristic
621C2#1307843211yescharacteristic
622C2#1307843911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#423C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#423D11
hypocenterC11#23617
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. C2×#10622734C2semidirect
5. C2×#10622541C2semidirect
6. #13070010C2semidirect
7. #13070003C2semidirect
8. #13069996C2semidirect
9. #13069989C2semidirect
10. #13068336C2semidirect
11. C2×C11×#423C2semidirect
198. C2×#423D11semidirect
507. C11#23617semidirect

Maximal subgroups

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

subgroupindex
C2×#106227342
C2×#106227462
#130711062
C2×#106225412
#130700102
#130700032
#130699962
#130699892
#130683362
C2×C11×#4232
#2361711