Finite Group Databasebeta

← #14795040

Subgroups — #14795040

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622622C211yesmaximal, characteristic, complemented
2C2×#10622448C211yesmaximal, characteristic, complemented
3#13076927C211yesmaximal, characteristic, complemented
4C4×#66991C211yesmaximal, characteristic
5#13070054C211yesmaximal, characteristic, complemented
6#13070043C211yesmaximal, characteristic, complemented
7#13069803C211yesmaximal, characteristic
8#13069796C211yesmaximal, characteristic
9#13069571C211yesmaximal, characteristic, complemented
10#13069382C211yesmaximal, characteristic, complemented
11#13069358C211yesmaximal, characteristic, complemented
12#13069353C211yesmaximal, characteristic, complemented
13#13069315C211yesmaximal, characteristic, complemented
14#13069315C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×C42×D11C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#382C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C4×C22⋊Dic11—21no—
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33#10622622—24no—
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622569—21no—
45#10622557—21no—
46C4×C4⋊Dic11C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48#10622448—24no—
49#10622281—21no—
50#10622281—21no—
51#10622266—21no—
52#10622266—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×C22⋊D11—21no—
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66991—22no—
80#66991—22no—
81C4×C22⋊D11—44no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C42×D11—22no—
101C42×D11—22no—
102#66923—22no—
103#66923—22no—
104C11×C4⋊C8—22no—
105C11×#102—22no—
106C11×#102—22no—
107C11×#95—21no—
108C11×#95—21no—
109#66896—22no—
110#66896—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118(C2×D11)⋊C8—22no—
119(C2×D11)⋊C8—22no—
120#66879—22no—
121#66879—22no—
122#66872—22no—
123#66872—22no—
124#66871—22no—
125#66871—22no—
126C4⋊(C11⋊C8)D414yescomplemented
127#24706—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11#4112yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—24no—
146C2×C22⋊D11—42no—
147C2×C22⋊D11—42no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—41no—
165C2×C4×D11—41no—
166C2×C4×D11—41no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C22⋊C4—42no—
180C42×C11C2×D412yes—
181C42×C11#4112yes—
182C22⋊Dic11—24no—
183C22⋊Dic11—42no—
184C22⋊Dic11—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201C4×Dic11—22no—
202C4×Dic11—22no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—42no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×D412yes—
211C2×C11⋊C8C2×D412yes—
212C2×#478—111no—
213C2×#432—111no—
214#2851—111no—
215C4×#121—111no—
216#2077—111no—
217#2075—111no—
218#2034—111no—
219#2033—111no—
220#1989—111no—
221#1949—111no—
222#1944—111no—
223#1943—111no—
224#1936—111no—
225#1936—111no—
226#1804D1111yescharacteristic, complemented
227C23×C11—22no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11C22×D411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11AGL(1,ℤ/8)12yes—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—41no—
245D4×C11—41no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—84no—
260C2×C4×C11#12112yes—
261C2×C4×C11#12112yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C22⋊D11—48no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C4×D11—44no—
291C4×D11—44no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C11⋊C8—22no—
299C11⋊C8—22no—
300C2×#125—111no—
301C2×#121—111no—
302C2×C4×D4—221no—
303C2×C4×D4C2×D1111yescharacteristic
304C22×C42—111no—
305#478—224no—
306#432—224no—
307C2×#107—111no—
308C2×#107—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8C2×D1111yescharacteristic
313C2×#102—111no—
314C2×#102—111no—
315C2×#102C2×D1111yescharacteristic
316C2×#102C2×D1111yescharacteristic
317C2×C22⋊C8—111no—
318C2×C22⋊C8—111no—
319C2×#97—111no—
320C2×#97—111no—
321#390—111no—
322#389—111no—
323#389—111no—
324#389—111no—
325#388—221no—
326#387—221no—
327#387—221no—
328#386—221no—
329#385—221no—
330#385—221no—
331#382C2×D1111yescharacteristic
332#380—111no—
333#380—111no—
334#380—111no—
335C4×C4⋊C4—111no—
336C4×C22⋊C4—221no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11C2×#12111yescharacteristic
353C22×C11#52511yescharacteristic
354C22×C11#53611yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57511yescharacteristic
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C4×C11—22no—
367C4×C11—22no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11#54711yescharacteristic
372C4×C11#54811yescharacteristic
373C4×C11#55211yescharacteristic
374C4×C11#55611yescharacteristic
375Dic11—42no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379Dic11—81no—
380Dic11—81no—
381Dic11—81no—
382C22×D4—221no—
383C22×D4C22×D1111yescharacteristic
384C23×C4—21no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392#125—222no—
393#125—222no—
394#121—222no—
395#121—222no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—444no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—222no—
422C2×C42—222no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425#107—222no—
426#107—222no—
427#106—222no—
428#106—222no—
429C4⋊C8—22no—
430C4⋊C8—114no—
431#102—22no—
432#102—22no—
433#102—222no—
434#102—222no—
435C22⋊C8—222no—
436C22⋊C8—222no—
437#97—222no—
438#97—222no—
439#95—21no—
440#95—21no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11—82no—
449C2×C11#241511yescharacteristic
450C2×C11#305411yescharacteristic
451C2×C11#305511yescharacteristic
452C2×C11#311111yescharacteristic
453C2×C11#311411yescharacteristic
454C2×C11#323411yescharacteristic
455C2×C11#324011yescharacteristic
456D11—42no—
457C24—21no—
458C24—111no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—224no—
465C2×D4—442no—
466C2×D4—442no—
467C2×D4#434112yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—441no—
491C22×C4—441no—
492C22×C4—441no—
493C22×C4D4×D1111yescharacteristic
494C22×C4D4×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—112no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C22⋊C4—42no—
528C22⋊C4—224no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C42—222no—
535C42—222no—
536C42—221no—
537C42—221no—
538C42—442no—
539C42#433912yes—
540C42D4×D1112yes—
541C11#2470611yescharacteristic, complemented, Sylow
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—112no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23C2×D4×D1111yescharacteristic
557D4—22no—
558D4—22no—
559D4—41no—
560D4—41no—
561D4—448no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—221no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4#6693712yes—
604C2×C4#6693712yes—
605C2×C4C2×#433911yescharacteristic
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4C2×#434111yescharacteristic
608C2×C4#6704011yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704311yescharacteristic
611C8—41no—
612C8—41no—
613C8—222no—
614C8—222no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—222no—
623C22—222no—
624C22—222no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22C2×#6693711yescharacteristic
630C22#1062313711yescharacteristic
631C22#1062315911yescharacteristic
632C22#1062329911yescharacteristic
633C22#1062329911yescharacteristic
634C22D11×AGL(1,ℤ/8)11yescharacteristic
635C22#1062330411yescharacteristic
636C4—22no—
637C4—22no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4—441no—
642C4—441no—
643C4—441no—
644C4—442no—
645C4—881no—
646C4—881no—
647C4—881no—
648C4#1062304411yescharacteristic
649C4#1062306411yescharacteristic
650C4#1062312911yescharacteristic
651C4#1062316211yescharacteristic
652C2—82no—
653C2—442no—
654C2#1307204711yescharacteristic
655C2#1307822411yescharacteristic
656C2#1307823311yescharacteristic
657C2#1307872211yescharacteristic
658C2#1307875311yescharacteristic
659C2#1307980411yescharacteristic
660C2#1307985511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#1804D11
hypocenterC11#24706
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. C2×#10622622C2semidirect
2. C2×#10622448C2semidirect
3. #13076927C2semidirect
5. #13070054C2semidirect
6. #13070043C2semidirect
9. #13069571C2semidirect
10. #13069382C2semidirect
11. #13069358C2semidirect
12. #13069353C2semidirect
13. #13069315C2semidirect
14. #13069315C2semidirect
15. C11×#1804C2semidirect
126. C4⋊(C11⋊C8)D4semidirect
226. #1804D11semidirect
541. C11#24706semidirect

Maximal subgroups

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

subgroupindex
C2×#106226222
C2×#106224482
#130769272
C4×#669912
#130700542
#130700432
#130698032
#130697962
#130695712
#130693822
#130693582
#130693532
#130693152
C11×#18042
#2470611