Finite Group Databasebeta

← #14764900

Subgroups — #14764900

Order 2816.

1308 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×#10622649C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3#13069481C212yesmaximal, complemented
4#13069298C212yesmaximal, complemented
5#13069236C212yesmaximal, complemented
6#13068964C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic, complemented
8#13068803C211yesmaximal, characteristic, complemented
9#13068546C211yesmaximal, characteristic, complemented
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C4×C11×#121C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C22×#4323C2212yes—
18C22×(C2×D11)⋊C4—21no—
19C22×(C2×D11)⋊C4—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C11×#390C2211yescharacteristic, complemented
22C11×#389C2211yescharacteristic, complemented
23C11×#388—21no—
24C11×#386—21no—
25C11×#380C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic, complemented
27C4×C11×C22⋊C4—21no—
28C2×#66896C2212yescomplemented
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622649C418yescomplemented
32C2×#66873C2212yes—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35C2×#66871C2212yescomplemented
36#10622552—21no—
37#10622552—21no—
38#10622552C2212yes—
39#10622552C2212yes—
40C2×C4×C11⋊C8C2212yescomplemented
41#10622167C2212yescomplemented
42#10622167C2212yescomplemented
43#10622162C2212yescomplemented
44C24×D11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C22×D44—21no—
53C22×D44—22no—
54C22×D44—42no—
55C22×D44—42no—
56C22×D44C2×C414yescomplemented
57C22×D44C2312yes—
58C11×#121—22no—
59C11×#121C2×C414yes—
60C4×D4×C11—42no—
61C4×D4×C11—44no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11—42no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×#4323—42no—
78C2×#4323—42no—
79C2×#4323C2×C418yescomplemented
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4—44no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—42no—
88C2×C4⋊Dic11C2312yes—
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2312yes—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94#66896—42no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)C2×C414yescomplemented
97#66873—42no—
98#66873—42no—
99#66873C2×C418yescomplemented
100#66871—42no—
101C4×C11⋊C8—42no—
102#22040—111nomaximal, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C23×D11—24no—
106C23×D11—22no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11—42no—
111C23×D11—42no—
112C23×D11—42no—
113C2×D4×C11—24no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11C22×C412yes—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11D814yescomplemented
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—22no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C2×D44—24no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—48no—
153C2×D44—42no—
154C2×D44—42no—
155C2×D44—48no—
156C2×D44C22×C414yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4C22×C412yes—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—41no—
170C42×C11—41no—
171C42×C11—42no—
172#4323—48no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—44no—
175(C2×D11)⋊C4—44no—
176(C2×D11)⋊C4—44no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8C22×C414yes—
186C2×#447—111no—
187C4×#121D1111yescharacteristic, complemented
188C2×#390—111no—
189#1970—112no—
190#1934—112no—
191#1925—112no—
192#1879—112no—
193#1874—111no—
194#1852—111no—
195#1786—111no—
196C4×C22⋊C8—111no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11C4×D412yes—
209C23×C11C2×D812yes—
210C23×C11#13512yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—48no—
214C22×D11—48no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—48no—
222C22×D11—84no—
223C22×D11—84no—
224C22×D11—84no—
225C22×D11—84no—
226D4×C11—24no—
227D4×C11—48no—
228D4×C11—42no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—84no—
254C2×C4×C11C4×D412yes—
255C2×C4×C11C2×D812yes—
256C2×C4×C11C2×D812yes—
257C2×C4×C11AGL(1,ℤ/8)12yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)12yes—
261C2×C4×C11H(5,𝔽2)12yes—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—84no—
266D44—24no—
267D44—24no—
268D44—48no—
269D44—42no—
270D44—42no—
271C11⋊C8—24no—
272C11⋊C8—42no—
273C23×D4—111no—
274C22×D8—112no—
275C2×#121C2×D1111yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C2×D1111yescharacteristic, complemented
278C22×C4⋊C4—111no—
279C22×C22⋊C4—221no—
280C22×C22⋊C4—221no—
281C22×C42C2×D1111yescharacteristic
282#447—118no—
283C2×#107—112no—
284C2×#102—112no—
285C2×#102—112no—
286C2×#102—112no—
287C2×#102—112no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×C4×C8—112no—
291#390—112no—
292#390—112no—
293#390—221no—
294#390—221no—
295#390C2×D1111yescharacteristic, complemented
296#389C2×D1111yescharacteristic, complemented
297#388—21no—
298#386—21no—
299#380C2×D1111yescharacteristic
300C4×C4⋊C4C2×D1111yescharacteristic, complemented
301C4×C22⋊C4—21no—
302#340—112no—
303#340—112no—
304#336—112no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11C4×D814yes—
319C22×C11C2×C4×D411yescharacteristic
320C22×C11#53411yescharacteristic
321C22×C11#53511yescharacteristic
322C22×C11C22×D811yescharacteristic
323C22×C11C2×#13511yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11#57511yescharacteristic
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—816no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—82no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#51812yes—
343C4×C11#53812yes—
344Dic11—82no—
345C25—221no—
346C22×D4—21no—
347C22×D4—114no—
348C22×D4—112no—
349C22×D4—222no—
350C22×D4—221no—
351C22×D4—442no—
352C22×D4—442no—
353C22×D4C22×D1111yescharacteristic
354C23×C4—21no—
355C23×C4—221no—
356C23×C4C22⋊D1111yescharacteristic
357C23×C4C22⋊D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C2×D8—118no—
360C2×D8—442no—
361C2×D8—442no—
362C22×C8—112no—
363C22×C8—112no—
364#121—22no—
365#121C4×D1114yes—
366C4×D4—42no—
367C4×D4—44no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—442no—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4—444no—
386C2×C42—21no—
387C2×C42—42no—
388C2×C42C22⋊D1111yescharacteristic
389C2×C42C22⋊D1111yescharacteristic
390C2×C42C22×D1111yescharacteristic
391C2×C42C22×D1111yescharacteristic
392#107—442no—
393#102—118no—
394#102—442no—
395#102—442no—
396#102—442no—
397C22⋊C8—114no—
398C22⋊C8—222no—
399C4×C8—442no—
400#95—21no—
401#95—21no—
402#95—21no—
403C2×C11—24no—
404C2×C11—82no—
405C2×C11#232111yescharacteristic
406C2×C11C2×C4×D811yescharacteristic
407C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C11#318611yescharacteristic
409C2×C11#318811yescharacteristic
410C2×C11#320511yescharacteristic
411C2×C11#321111yescharacteristic
412D11—84no—
413C24—21no—
414C24—224no—
415C24—222no—
416C24—442no—
417C24—442no—
418C24—442no—
419C24—442no—
420C24—442no—
421C24—442no—
422C24C2×C22⋊D1111yescharacteristic
423C2×D4—24no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—114no—
430C2×D4—224no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—448no—
437C2×D4—442no—
438C2×D4—442no—
439C2×D4—448no—
440C2×D4C2×C4×D1112yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—222no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4#432314yescomplemented
459C22×C4C2×C4×D1112yes—
460C22×C4#433912yes—
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C23×D1111yescharacteristic
467D8—448no—
468C2×C8—114no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—222no—
472C2×C8—222no—
473C2×C8—222no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—42no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—442no—
481C4⋊C4C2×C4×D1112yes—
482C22⋊C4—24no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—444no—
488C22⋊C4—444no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C42—22no—
492C42—22no—
493C42—41no—
494C42—41no—
495C42—42no—
496C11#2204011yescharacteristic, complemented, Sylow
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—224no—
509C23—448no—
510C23—448no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—448no—
518C23—884no—
519C23—884no—
520C23—884no—
521C23—884no—
522C23C4×C22⋊D1112yes—
523C23C2×#432312yes—
524C23#6700312yes—
525C23C22×C22⋊D1111yescharacteristic
526D4—24no—
527D4—48no—
528D4—42no—
529D4—224no—
530D4—224no—
531D4—448no—
532D4—442no—
533D4—442no—
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—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—84no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—884no—
563C2×C4C4×C22⋊D1112yes—
564C2×C4C2×#432312yes—
565C2×C4C2×#432312yes—
566C2×C4#6700212yes—
567C2×C4C22×C4×D1111yescharacteristic
568C2×C4C2×#433911yescharacteristic
569C2×C4#6703712yes—
570C2×C4#6704212yes—
571C8—224no—
572C8—442no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—444no—
587C22—444no—
588C22—444no—
589C22—8816no—
590C22—882no—
591C22—882no—
592C22—882no—
593C22—882no—
594C22C4×#432314yes—
595C22C2×C4×C22⋊D1111yescharacteristic
596C22C22×#432311yescharacteristic
597C22#1062333511yescharacteristic
598C22C2×#6700211yescharacteristic
599C22C2×#6700311yescharacteristic
600C22#1062335311yescharacteristic
601C22#1062336111yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—41no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—882no—
611C4#1062307612yes—
612C4#1062309112yes—
613C2—24no—
614C2—82no—
615C2—884no—
616C2#1307127011yescharacteristic
617C2C2×C4×#432311yescharacteristic
618C2C4×#6700211yescharacteristic
619C2#1307936411yescharacteristic
620C2#1307937711yescharacteristic
621C2#1307953111yescharacteristic
622C2#1307957711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#22040
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. #13069481C2semidirect
4. #13069298C2semidirect
5. #13069236C2semidirect
6. #13068964C2semidirect
7. #13068934C2semidirect
8. #13068803C2semidirect
9. #13068546C2semidirect
10. C4×C22⋊(C11⋊C8)C2semidirect
11. C4×C11×#121C2semidirect
15. C2×C4×D4×C11C22semidirect
21. C11×#390C22semidirect
22. C11×#389C22semidirect
26. C4×C11×C4⋊C4C22semidirect
28. C2×#66896C22semidirect
31. #10622649C4semidirect
35. C2×#66871C22semidirect
40. C2×C4×C11⋊C8C22semidirect
41. #10622167C22semidirect
42. #10622167C22semidirect
43. #10622162C22semidirect
56. C22×D44C2×C4semidirect
79. C2×#4323C2×C4semidirect
96. C22⋊(C11⋊C8)C2×C4semidirect
99. #66873C2×C4semidirect
133. C22×C4×C11D8semidirect
187. C4×#121D11semidirect
277. C2×C4×D4C2×D11semidirect
295. #390C2×D11semidirect
296. #389C2×D11semidirect
300. C4×C4⋊C4C2×D11semidirect
458. C22×C4#4323semidirect
496. C11#22040semidirect

Maximal subgroups

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

subgroupindex
C2×#106226492
C2×#106225522
#130694812
#130692982
#130692362
#130689642
#130689342
#130688032
#130685462
C4×C22⋊(C11⋊C8)2
C4×C11×#1212
#2204011