Finite Group Databasebeta

← #14769419

Subgroups — #14769419

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic
2C2×#10622625C211yesmaximal, characteristic, complemented
3C2×#10622579C212yesmaximal, complemented
4#13069539C211yesmaximal, characteristic, complemented
5#13069417C211yesmaximal, characteristic, complemented
6#13069047C212yesmaximal, complemented
7#13068923C212yesmaximal, complemented
8#13068613C211yesmaximal, characteristic, complemented
9#13068554C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C2×#66991—21no—
17C2×#66977C2212yes—
18C22×#4318C2212yes—
19#10623082—24no—
20#10623082C418yescomplemented
21C2×C4⋊C4×D11—21no—
22C2×#66936—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C11×#389—21no—
26C11×#385—22no—
27C11×#384C2211yescharacteristic
28C11×#380C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622625—24no—
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36#10622579—28no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2212yes—
39C2×#66873C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11C2312yes—
48C22×C22⋊D11—22no—
49C2×#4339—24no—
50C2×#4339—24no—
51C2×#4339—24no—
52C2×#4339—42no—
53C2×#4339—42no—
54C2×#4339C2×C418yescomplemented
55C22×D44C2311yescharacteristic
56C22×C4×D11—21no—
57C22×C4×D11—22no—
58C22×Dic22C2312yes—
59C4×D4×C11—44no—
60C4×D4×C11C2×C414yes—
61C4×D4×C11D414yes—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—42no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4D412yes—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—22no—
76#66991—28no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81#66977—24no—
82#66977C2×C418yescomplemented
83C2×Dic11⋊C4—22no—
84C2×#4318—24no—
85C2×#4318—24no—
86C2×#4318—42no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C4⋊C4×D11—28no—
91#66936—216no—
92C4×D44—22no—
93C4×D44C2×C414yescomplemented
94#66922—22no—
95#66922C2×C414yescomplemented
96C11×#95—21no—
97C11×#95—22no—
98C22⋊(C11⋊C8)—24no—
99#66874—24no—
100#66874—24no—
101#66874—42no—
102#66874—42no—
103#66873—24no—
104#66873—22no—
105#66873D414yescomplemented
106C4⋊(C11⋊C8)—22no—
107C4×C11⋊C8—22no—
108#22431—111nomaximal, Sylow
109C24×C11C2×D412yes—
110C23×D11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11C22⋊C414yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—82no—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—28no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—44no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135#4339—216no—
136#4339—48no—
137#4339—48no—
138#4339—48no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44C22×C412yes—
143C2×D44C2×D412yes—
144C2×D44#4112yes—
145C2×C4×D11—24no—
146C2×C4×D11—28no—
147C2×C4×D11—44no—
148C2×C4×D11—44no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22C22×C414yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4C22⋊C414yes—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—44no—
168C11×C22⋊C4C22⋊C418yes—
169C42×C11—42no—
170C42×C11C22×C412yes—
171C42×C11C2×D412yes—
172C22⋊Dic11—28no—
173(C2×D11)⋊C4—24no—
174C4⋊Dic11—24no—
175C4⋊Dic11—24no—
176C4⋊Dic11—21no—
177C4⋊Dic11C22×C412yes—
178Dic11⋊C4—28no—
179#4318—48no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2×D412yes—
189C2×#547—111no—
190C2×#436—111no—
191C2×#417—112no—
192D4×C4⋊C4D1111yescharacteristic, complemented
193#1981—111no—
194#1956—111no—
195#1894—112no—
196#1872—112no—
197#1802—111no—
198#1788—112no—
199C4×#102—111no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11C2×C22⋊C414yes—
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215D4×C11—28no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—88no—
234C2×C4×C11C2×C22⋊C414yes—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11#13712yes—
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C22⋊D11—416no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252D44—22no—
253D44—22no—
254D44—22no—
255D44C4×D414yescomplemented
256C4×D11—416no—
257C4×D11—48no—
258Dic22—24no—
259Dic22—24no—
260Dic22—42no—
261Dic22—42no—
262C11⋊C8—22no—
263C11⋊C8—42no—
264C11⋊C8—41no—
265C22×#41—112no—
266C22×M16—112no—
267#547—118no—
268#547—224no—
269C2×C4⋊Q8—111no—
270C2×#123—222no—
271C2×C22⋊Q8—112no—
272C2×#121—221no—
273C2×C4×D4—21no—
274C2×C4×D4—111no—
275C2×C4×D4C2×D1111yescharacteristic
276C22×C4⋊C4—221no—
277C22×C4⋊C4C2×D1112yes—
278#436—224no—
279C2×C4⋊C8—111no—
280#417—228no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#102—111no—
286C2×#102—112no—
287C2×#102—111no—
288C2×C22⋊C8—112no—
289C2×C4×C8—111no—
290#389—21no—
291#385—22no—
292#384C2×D1111yescharacteristic
293#380C2×D1112yes—
294C4×C4⋊C4C2×D1111yescharacteristic
295#340—112no—
296#340—111no—
297#340—111no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11C22×C22⋊C411yescharacteristic
306C22×C11D4211yescharacteristic
307C22×C11#54611yescharacteristic
308C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C11C2×#13711yescharacteristic
310C22×C11#57711yescharacteristic
311C22×C11#57811yescharacteristic
312C2×D11—24no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C4×C11—24no—
320C4×C11—22no—
321C4×C11—42no—
322C4×C11—81no—
323C4×C11—82no—
324C4×C11#41714yescomplemented
325C4×C11C2×C4×D411yescharacteristic
326C4×C11#51811yescharacteristic
327C4×C11D4211yescharacteristic
328C4×C11#54611yescharacteristic
329Dic11—44no—
330Dic11—42no—
331C2×#41—118no—
332C2×#41—224no—
333C2×#41—224no—
334C2×#41—224no—
335C2×#41—442no—
336C2×#41—442no—
337C22×Q8—112no—
338C22×D4—111no—
339C22×D4—222no—
340C22×D4C22⋊D1111yescharacteristic
341C23×C4—22no—
342C23×C4—221no—
343C23×C4—222no—
344C23×C4C22×D1112yes—
345C2×M16—224no—
346C2×M16—224no—
347C2×M16—442no—
348C22×C8—111no—
349C22×C8—112no—
350C22×C8—111no—
351C4⋊Q8—114no—
352C4⋊Q8—222no—
353#123—2216no—
354C22⋊Q8—118no—
355C22⋊Q8—224no—
356#121—228no—
357C4×D4—44no—
358C4×D4—114no—
359C4×D4—222no—
360C4×D4C4×D1114yes—
361C4×D4D4414yes—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—228no—
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22×D1112yes—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—22no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4C22⋊D1112yes—
380C2×C42—21no—
381C2×C42C22×D1111yescharacteristic
382C4⋊C8—222no—
383#103—224no—
384#103—224no—
385#103—442no—
386#103—442no—
387#102—114no—
388#102—222no—
389#102—224no—
390C22⋊C8—224no—
391C4×C8—222no—
392#95—21no—
393#95—22no—
394C2×C11—44no—
395C2×C11D4×C22⋊C411yescharacteristic
396C2×C11C2×#41711yescharacteristic
397C2×C11#289811yescharacteristic
398C2×C11#327211yescharacteristic
399C2×C11#327611yescharacteristic
400C2×C11#333011yescharacteristic
401C2×C11#333111yescharacteristic
402D11—44no—
403C24—221no—
404C24C2×C22⋊D1112yes—
405#41—2216no—
406#41—448no—
407#41—448no—
408#41—448no—
409C2×Q8—114no—
410C2×Q8—222no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—112no—
418C2×D4—112no—
419C2×D4—112no—
420C2×D4—228no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—444no—
425C2×D4—444no—
426C2×D4(C2×D11)⋊C414yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—82no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—224no—
440C22×C4—228no—
441C22×C4—444no—
442C22×C4—444no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4C2×C4×D1114yes—
446C22×C4C2×D4414yes—
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451M16—448no—
452C2×C8—112no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—222no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—44no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—112no—
470C4⋊C4—224no—
471C4⋊C4—228no—
472C4⋊C4—224no—
473C4⋊C4—221no—
474C4⋊C4(C2×D11)⋊C414yes—
475C4⋊C4D4×D1112yes—
476C22⋊C4—44no—
477C22⋊C4—228no—
478C22⋊C4—224no—
479C22⋊C4(C2×D11)⋊C418yes—
480C42—42no—
481C42C2×C4×D1112yes—
482C42C2×D4412yes—
483C11#2243111yescharacteristic, complemented, Sylow
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—222no—
491C23—222no—
492C23—222no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23C2×(C2×D11)⋊C414yes—
498C23C22×C22⋊D1111yescharacteristic
499Q8—224no—
500Q8—224no—
501Q8—442no—
502Q8—442no—
503D4—28no—
504D4—114no—
505D4—222no—
506D4—222no—
507D4—222no—
508D4—4416no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—88no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—4416no—
530C2×C4—441no—
531C2×C4—442no—
532C2×C4—441no—
533C2×C4—442no—
534C2×C4—448no—
535C2×C4C2×(C2×D11)⋊C412yes—
536C2×C4C2×(C2×D11)⋊C414yes—
537C2×C4C2×(C2×D11)⋊C412yes—
538C2×C4#6698512yes—
539C2×C4#6699512yes—
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C22×D4411yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4#6703711yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#6704211yescharacteristic
546C8—222no—
547C8—442no—
548C8—441no—
549C22—24no—
550C22—24no—
551C22—24no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—224no—
557C22—442no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—442no—
562C22—442no—
563C22C22×(C2×D11)⋊C411yescharacteristic
564C22C2×#6698511yescharacteristic
565C22D4×C22⋊D1111yescharacteristic
566C22C2×#6699511yescharacteristic
567C22#1062336011yescharacteristic
568C22#1062336711yescharacteristic
569C22#1062336911yescharacteristic
570C4—24no—
571C4—22no—
572C4—42no—
573C4—81no—
574C4—82no—
575C4—444no—
576C4—442no—
577C4#1062257914yescomplemented
578C4C4×D4×D1111yescharacteristic
579C4#1062307611yescharacteristic
580C4D4×D4411yescharacteristic
581C4#1062308511yescharacteristic
582C2—44no—
583C2—444no—
584C2D4×(C2×D11)⋊C411yescharacteristic
585C2C2×#1062257911yescharacteristic
586C2#1307714611yescharacteristic
587C2#1308021211yescharacteristic
588C2#1308026211yescharacteristic
589C2#1308091511yescharacteristic
590C2#1308092611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22431
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622625C2semidirect
3. C2×#10622579C2semidirect
4. #13069539C2semidirect
5. #13069417C2semidirect
6. #13069047C2semidirect
7. #13068923C2semidirect
8. #13068613C2semidirect
9. #13068554C2semidirect
10. C4×#66873C2semidirect
11. D4×C11×C4⋊C4C2semidirect
20. #10623082C4semidirect
54. C2×#4339C2×C4semidirect
82. #66977C2×C4semidirect
93. C4×D44C2×C4semidirect
95. #66922C2×C4semidirect
105. #66873D4semidirect
192. D4×C4⋊C4D11semidirect
255. D44C4×D4semidirect
324. C4×C11#417semidirect
483. C11#22431semidirect
577. C4#10622579semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106226252
C2×#106225792
#130695392
#130694172
#130690472
#130689232
#130686132
#130685542
C4×#668732
D4×C11×C4⋊C42
#2243111