Finite Group Databasebeta

← #14764983

Subgroups — #14764983

Order 2816.

1296 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
2#121×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622601C211yesmaximal, characteristic, complemented
4#13069489C212yesmaximal, complemented
5#13069314C212yesmaximal, complemented
6#13069241C212yesmaximal, complemented
7#13068962C212yesmaximal, complemented
8#13068809C211yesmaximal, characteristic, complemented
9#13068548C211yesmaximal, characteristic, complemented
10#13068380C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×D4×Dic11—21no—
16C2×D4×Dic11C2211yescharacteristic, complemented
17C22×#4323C2212yes—
18C22×(C2×D11)⋊C4—21no—
19C22×(C2×D11)⋊C4—21no—
20C22×C4×Dic11C2211yescharacteristic
21C2×C11×#102C2212yescomplemented
22C2×C11×C22⋊C8C2211yescharacteristic
23#10622834C2211yescharacteristic, complemented
24#10622833—21no—
25#10622825C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×#66885C2212yes—
28C2×#66885C2212yes—
29C2×#66879C2212yescomplemented
30#10622649C418yescomplemented
31#10622601—21no—
32#10622601—21no—
33#10622601C2212yes—
34#10622601C2212yes—
35#10622598C2211yescharacteristic, complemented
36C4⋊C4×Dic11C2211yescharacteristic, complemented
37C2×#66873C2212yes—
38C2×#66872C2212yescomplemented
39#10622564—21no—
40C22⋊C4×Dic11—21no—
41C11×#340C2212yescomplemented
42#10622188C2212yescomplemented
43#10622167C2212yescomplemented
44C24×D11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C23×Dic11D411yescharacteristic
51C23×Dic11D411yescharacteristic
52C22×D44—21no—
53C22×D44—22no—
54C22×D44—42no—
55C22×D44—42no—
56C22×D44C2×C414yescomplemented
57C22×D44C2312yes—
58C22×C8×C11C2312yes—
59C11×#121—22no—
60C11×#121C2×C414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70D4×Dic11—42no—
71D4×Dic11—44no—
72C2×#4323—42no—
73C2×#4323—42no—
74C2×#4323C2×C418yescomplemented
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—44no—
80C2×(C2×D11)⋊C4—44no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4×Dic11—21no—
85C2×C4×Dic11—42no—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2312yes—
91C11×#102—42no—
92C11×C22⋊C8—22no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C22⋊(C11⋊C8)C2×C414yescomplemented
97#66885—42no—
98#66885—42no—
99#66879—42no—
100#66873C2×C418yescomplemented
101#66872—42no—
102#22046—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—21no—
123C22×C4×C11—22no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—41no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
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—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4C22×C412yes—
165C11×C22⋊C4—24no—
166C22⋊Dic11—42no—
167C22⋊Dic11—42no—
168C22⋊Dic11—42no—
169C22⋊Dic11—42no—
170#4323—48no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—44no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—42no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—41no—
181C4×Dic11—41no—
182C4×Dic11—42no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8C22×C414yes—
186C2×#447—111no—
187C4×#121—111no—
188C2×#390—111no—
189#1972—112no—
190#1936—112no—
191#1926—112no—
192#1879—112no—
193#1874D1111yescharacteristic, complemented
194#1853—111no—
195#1786—111no—
196#1749—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×C11AGL(1,ℤ/8)12yes—
210C23×C11AGL(1,ℤ/8)12yes—
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—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—84no—
240C2×C4×C11C4×D412yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)12yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—84no—
265C2×Dic11AGL(1,ℤ/8)12yes—
266D44—24no—
267D44—24no—
268D44—48no—
269D44—42no—
270D44—42no—
271C8×C11—42no—
272C11⋊C8—24no—
273C23×D4—111no—
274C22×D8—112no—
275C2×#121C2×D1111yescharacteristic
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4—221no—
280C22×C22⋊C4—221no—
281C22×C42—111no—
282#447—118no—
283C2×#106—112no—
284C2×#102—112no—
285C2×#102—112no—
286C2×#102—112no—
287C2×#102C2×D1112yescomplemented
288C2×C22⋊C8—111no—
289C2×C22⋊C8C2×D1111yescharacteristic
290C2×#97—112no—
291#390—111no—
292#390—112no—
293#390—112no—
294#390—221no—
295#390—221no—
296#389—111no—
297#388—221no—
298#386—221no—
299#380—111no—
300C4×C4⋊C4—111no—
301C4×C22⋊C4—221no—
302#340—112no—
303#340C2×D1112yescomplemented
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×C11#44214yes—
319C22×C11C2×C4×D411yescharacteristic
320C22×C11#53411yescharacteristic
321C22×C11#53511yescharacteristic
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
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—42no—
336C4×C11—82no—
337C4×C11#51812yes—
338C4×C11#53812yes—
339Dic11—22no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345C25—221no—
346C22×D4—21no—
347C22×D4—114no—
348C22×D4—112no—
349C22×D4—221no—
350C22×D4—222no—
351C22×D4—442no—
352C22×D4—442no—
353C22×D4C22×D1111yescharacteristic
354C23×C4—21no—
355C23×C4—111no—
356C23×C4—111no—
357C23×C4—221no—
358C23×C4C22×D1111yescharacteristic
359C2×D8—118no—
360C2×D8—442no—
361C2×D8—442no—
362C22×C8—112no—
363C22×C8C22×D1112yes—
364#121—22no—
365#121C4×D1114yes—
366C4×D4—442no—
367C4×D4—444no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1112yes—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4—444no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—221no—
391C2×C42—442no—
392#106—442no—
393#102—42no—
394#102—118no—
395#102—442no—
396#102—442no—
397C22⋊C8—22no—
398C22⋊C8—114no—
399#97—442no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11—24no—
404C2×C11—82no—
405C2×C11#232111yescharacteristic
406C2×C11C2×#44211yescharacteristic
407C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C11#319211yescharacteristic
409C2×C11#319411yescharacteristic
410C2×C11#321311yescharacteristic
411C2×C11#321711yescharacteristic
412D11—84no—
413C24—21no—
414C24—224no—
415C24—222no—
416C24—442no—
417C24—442no—
418C24—442no—
419C24—442no—
420C24—442no—
421C24—442no—
422C24D4×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—21no—
444C22×C4—22no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—442no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4C2×C4×D1112yes—
464C22×C4D4×D1111yescharacteristic
465C22×C4#434112yes—
466C22×C4C23×D1111yescharacteristic
467D8—448no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—114no—
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—444no—
484C22⋊C4—444no—
485C22⋊C4—444no—
486C22⋊C4—444no—
487C22⋊C4—442no—
488C22⋊C4—442no—
489C22⋊C4—442no—
490C22⋊C4—442no—
491C42—222no—
492C42—222no—
493C42—441no—
494C42—441no—
495C42—442no—
496C11#2204611yescharacteristic, 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—448no—
517C23—442no—
518C23—884no—
519C23—884no—
520C23—884no—
521C23—884no—
522C23(C22⋊D11)⋊C412yes—
523C23#6696412yes—
524C23#6696712yes—
525C23C2×D4×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—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—84no—
545C2×C4—112no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—444no—
558C2×C4—444no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—884no—
566C2×C4(C22⋊D11)⋊C412yes—
567C2×C4C22×C4×D1111yescharacteristic
568C2×C4C2×#434111yescharacteristic
569C2×C4#6703712yes—
570C2×C4#6704212yes—
571C8—42no—
572C8—224no—
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—
594C22#1062239814yes—
595C22C2×(C22⋊D11)⋊C411yescharacteristic
596C22#1062312311yescharacteristic
597C22#1062318411yescharacteristic
598C22C2×#6696411yescharacteristic
599C22C2×#6696711yescharacteristic
600C22D11×AGL(1,ℤ/8)11yescharacteristic
601C22#1062330811yescharacteristic
602C4—22no—
603C4—42no—
604C4—82no—
605C4—222no—
606C4—441no—
607C4—441no—
608C4—441no—
609C4—881no—
610C4—881no—
611C4#1062307612yes—
612C4#1062314812yes—
613C2—24no—
614C2—82no—
615C2—884no—
616C2#1307127911yescharacteristic
617C2C2×#1062239811yescharacteristic
618C2#1307742911yescharacteristic
619C2#1307941511yescharacteristic
620C2#1307942911yescharacteristic
621C2#1307960211yescharacteristic
622C2#1307963211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
cosocleC22×C4×C11C24
hypercenter#1874D11
hypocenterC11#22046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. #121×Dic11C2semidirect
3. C2×#10622601C2semidirect
4. #13069489C2semidirect
5. #13069314C2semidirect
6. #13069241C2semidirect
7. #13068962C2semidirect
8. #13068809C2semidirect
9. #13068548C2semidirect
10. #13068380C2semidirect
11. C11×#1874C2semidirect
16. C2×D4×Dic11C22semidirect
21. C2×C11×#102C22semidirect
23. #10622834C22semidirect
29. C2×#66879C22semidirect
30. #10622649C4semidirect
35. #10622598C22semidirect
36. C4⋊C4×Dic11C22semidirect
38. C2×#66872C22semidirect
41. C11×#340C22semidirect
42. #10622188C22semidirect
43. #10622167C22semidirect
56. C22×D44C2×C4semidirect
74. C2×#4323C2×C4semidirect
96. C22⋊(C11⋊C8)C2×C4semidirect
100. #66873C2×C4semidirect
193. #1874D11semidirect
287. C2×#102C2×D11semidirect
303. #340C2×D11semidirect
496. C11#22046semidirect

Maximal subgroups

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

subgroupindex
C2×#106226492
#121×Dic112
C2×#106226012
#130694892
#130693142
#130692412
#130689622
#130688092
#130685482
#130683802
C11×#18742
#2204611