Finite Group Databasebeta

← #14755136

Subgroups — #14755136

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C22×C4×D44C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5#13068967C214yesmaximal, complemented
6#13068953C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068310C211yesmaximal, characteristic, complemented
9C11×#2297C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C23×C4×D11—21no—
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×#67002—24no—
16C2×#67002—24no—
17C2×#67002C418yescomplemented
18C22×#4325C2212yes—
19C22×#4323C2212yes—
20C22×(C2×D11)⋊C4—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C2×C4×D44—24no—
25C2×C4×D44—22no—
26C2×C4×D44—24no—
27C2×C4×D44C2214yes—
28C11×#391C2212yescomplemented
29C11×#390C2212yescomplemented
30C11×#386—21no—
31C11×#386—21no—
32C4×C11×C22⋊C4—22no—
33#10622845—24no—
34C2×#66899C2212yescomplemented
35C2×#66896C2212yescomplemented
36#10622614—24no—
37C2×#66873C2214yes—
38#10622167C2214yescomplemented
39#10622162C2214yescomplemented
40C24×D11—21no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41C2×C414yescomplemented
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C22×D44—22no—
56C22×D44—21no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44C2×C414yes—
60C22×D44D414yes—
61C22×D44D414yes—
62C22×D44C2312yes—
63C22×C4×D11—28no—
64C22×C4×D11—24no—
65C22×C4×D11—48no—
66C11×#117—22no—
67C11×#117—22no—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11—21no—
75C2×C42×C11D412yes—
76C2×C42×C11C2312yes—
77#67002—232no—
78C2×#4325—24no—
79C2×#4325—24no—
80C2×#4325C2×C418yescomplemented
81C2×#4323—24no—
82C2×#4323—24no—
83C2×#4323C2×C418yescomplemented
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—24no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11D414yes—
89C2×C4⋊Dic11C2312yes—
90C2×#4318—22no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318—22no—
95C2×#4318C2×C414yescomplemented
96C22×C11⋊C8C2312yes—
97C22×C11⋊C8C2312yes—
98C4×D44—216no—
99C4×D44—28no—
100C4×D44—28no—
101C11×#95—22no—
102C11×#95—22no—
103#66899—24no—
104#66896—24no—
105#66873—28no—
106#20925—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11C2×D411yescharacteristic
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—22no—
113C23×D11—44no—
114C23×D11—44no—
115C11×#41—28no—
116C11×#41—28no—
117C11×#41—44no—
118C11×#41—44no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11C22×C412yescomplemented
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11C22×C412yescomplemented
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—44no—
156C2×D44—28no—
157C2×D44—24no—
158C2×D44—24no—
159C2×D44—28no—
160C2×D44—24no—
161C2×D44—28no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44C22⋊C4116yescomplemented
166C2×D44C22×C414yes—
167C2×D44C2×D414yes—
168C2×D44C2×D414yes—
169C2×C4×D11—216no—
170C2×C4×D11—432no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C22⋊C4—44no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—44no—
178C42×C11—24no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—42no—
182#4325—216no—
183#4323—216no—
184(C2×D11)⋊C4—216no—
185C4⋊Dic11—24no—
186C4⋊Dic11—22no—
187C4⋊Dic11C2×D414yes—
188#4318—28no—
189#4318—44no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8C22×C414yescomplemented
196C22×AGL(1,ℤ/8)—111no—
197C22×C4×D4—111no—
198C2×#417—111no—
199C2×#418—111no—
200#2297D1111yescharacteristic, complemented
201#1879—114no—
202#1877—114no—
203#1736—111no—
204#1728—111no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C4×D412yes—
213C23×C11#12012yes—
214C23×C11#12112yes—
215C23×C11C22×D411yescharacteristic
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—216no—
220C22×D11—48no—
221C22×D11—416no—
222C22×D11—48no—
223C22×D11—416no—
224C22×D11—44no—
225C22×D11—44no—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—48no—
233D4×C11—41no—
234D4×C11—41no—
235C2×C4×C11—28no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—44no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11C2×C22⋊C414yes—
250C2×C4×C11C4×D414yes—
251C2×C4×C11C4×D412yes—
252C2×C4×C11#12012yes—
253C2×C4×C11#12114yes—
254C2×C4×C11#12112yes—
255C2×C4×C11#12314yes—
256C2×C4×C11AGL(1,ℤ/8)14yescomplemented
257C2×C4×C11C23×C411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×Dic11—24no—
264C2×Dic11—48no—
265C2×Dic11—44no—
266D44—24no—
267D44—24no—
268D44—24no—
269D44—216no—
270D44C2×C22⋊C418yes—
271C4×D11—432no—
272C11⋊C8—24no—
273C11⋊C8—42no—
274C22×#41C2×D1111yescharacteristic
275C23×D4—111no—
276C24×C4—221no—
277C2×AGL(1,ℤ/8)—118no—
278C2×AGL(1,ℤ/8)—224no—
279C2×AGL(1,ℤ/8)—224no—
280C22×SD16—112no—
281C22×D8—112no—
282C22×M16—111no—
283C22×M16—111no—
284C2×C4×D4—114no—
285C2×C4×D4—224no—
286C2×C4×D4—224no—
287C2×C4×D4—222no—
288C2×#117C2×D1111yescharacteristic
289C22×C4⋊C4—111no—
290C22×C22⋊C4—221no—
291C22×C42C2×D1111yescharacteristic
292#418—224no—
293#417—224no—
294C2×#103—112no—
295C2×#102—112no—
296C2×#102—114no—
297#391C2×D1112yescomplemented
298#390C2×D1112yescomplemented
299#386—21no—
300#386—21no—
301C4×C22⋊C4—22no—
302#340—114no—
303#336—114no—
304C22×C11—24no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—24no—
308C22×C11—44no—
309C22×C11—42no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—82no—
313C22×C11#38614yes—
314C22×C11C2×C4×D411yescharacteristic
315C22×C11C2×#12011yescharacteristic
316C22×C11C2×#12111yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)12yes—
318C22×C11#57512yes—
319C2×D11—28no—
320C2×D11—432no—
321C2×D11—48no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—48no—
325C4×C11—24no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—82no—
329C4×C11#38614yes—
330C4×C11C22×C22⋊C411yescharacteristic
331C4×C11C2×C4×D411yescharacteristic
332C4×C11C2×#12111yescharacteristic
333C4×C11C2×#12311yescharacteristic
334Dic11—44no—
335C25—221no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41C4×D1114yescomplemented
342C22×Q8C22×D1111yescharacteristic
343C22×D4—21no—
344C22×D4—114no—
345C22×D4—114no—
346C22×D4—114no—
347C22×D4—112no—
348C22×D4—222no—
349C22×D4—222no—
350C22×D4—222no—
351C22×D4—221no—
352C22×D4C22×D1111yescharacteristic
353C23×C4—21no—
354C23×C4—228no—
355C23×C4—221no—
356C23×C4—224no—
357C23×C4—448no—
358C23×C4C22⋊D1111yescharacteristic
359C23×C4C22⋊D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361AGL(1,ℤ/8)—2232no—
362C2×SD16—118no—
363C2×SD16—224no—
364C2×SD16—224no—
365C2×D8—118no—
366C2×D8—224no—
367C2×D8—224no—
368C2×M16—114no—
369C2×M16—222no—
370C2×M16—222no—
371C2×M16—222no—
372C2×M16—222no—
373C2×M16—222no—
374C22×C8—112no—
375C22×C8—112no—
376C4×D4—228no—
377C4×D4—228no—
378C4×D4—2216no—
379#117—22no—
380#117—22no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1112yes—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—224no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—21no—
394C2×C42C22⋊D1112yes—
395C2×C42C22×D1112yes—
396#103—224no—
397#102—228no—
398#102—224no—
399#95—22no—
400#95—22no—
401C2×C11—24no—
402C2×C11—82no—
403C2×C11C2×#38611yescharacteristic
404C2×C11C4×AGL(1,ℤ/8)12yes—
405C2×C11#300311yescharacteristic
406C2×C11#300511yescharacteristic
407C2×C11#303612yes—
408D11—48no—
409C24—21no—
410C24—224no—
411C24—224no—
412C24—224no—
413C24—222no—
414C24—444no—
415C24—444no—
416C24C2×C22⋊D1111yescharacteristic
417#41—28no—
418#41—28no—
419#41—44no—
420#41—44no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×C4×D1112yescomplemented
427C2×D4—24no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—1116no—
436C2×D4—114no—
437C2×D4—114no—
438C2×D4—114no—
439C2×D4—228no—
440C2×D4—228no—
441C2×D4—228no—
442C2×D4—224no—
443C2×D4—224no—
444C2×D4—224no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—222no—
448C2×D4C2×C4×D1112yescomplemented
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—2216no—
459C22×C4—224no—
460C22×C4—222no—
461C22×C4—4432no—
462C22×C4—448no—
463C22×C4—444no—
464C22×C4—448no—
465C22×C4C2×C4×D1112yes—
466C22×C4#433912yes—
467C22×C4D4×D1112yes—
468C22×C4D4×D1112yes—
469C22×C4D4×D1112yes—
470C22×C4#434112yes—
471C22×C4C2×C22⋊D1112yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—2216no—
476D8—2216no—
477M16—228no—
478M16—444no—
479C2×C8—114no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—222no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—114no—
488C4⋊C4—224no—
489C4⋊C4—222no—
490C22⋊C4—44no—
491C22⋊C4—42no—
492C22⋊C4—44no—
493C22⋊C4—2216no—
494C42—24no—
495C42—22no—
496C42—22no—
497C42—42no—
498C11#2092511yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—42no—
505C23—42no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—2216no—
510C23—448no—
511C23—4416no—
512C23—448no—
513C23—4416no—
514C23—444no—
515C23—444no—
516C23C4×C22⋊D1112yes—
517C23#6699012yes—
518C23#6699112yes—
519C23C22×C22⋊D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524D4—22no—
525D4—22no—
526D4—48no—
527D4—41no—
528D4—41no—
529D4—118no—
530D4—224no—
531D4—224no—
532D4—224no—
533D4—2216no—
534C2×C4—28no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—44no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—48no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—224no—
549C2×C4—4432no—
550C2×C4—448no—
551C2×C4—444no—
552C2×C4C22⋊C4×D1114yes—
553C2×C4(C22⋊D11)⋊C414yes—
554C2×C4#6693614yes—
555C2×C4#6693714yes—
556C2×C4C4×C22⋊D1112yes—
557C2×C4#6699012yes—
558C2×C4#6699112yes—
559C2×C4#6700214yescomplemented
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C8—224no—
567C8—442no—
568C22—24no—
569C22—22no—
570C22—22no—
571C22—24no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—81no—
576C22—81no—
577C22—228no—
578C22—4432no—
579C22—448no—
580C22—444no—
581C22—444no—
582C22—448no—
583C22#1062256914yes—
584C22C2×C4×C22⋊D1111yescharacteristic
585C22C2×#6699011yescharacteristic
586C22C2×#6699111yescharacteristic
587C22C2×#6700212yes—
588C22#1062335312yes—
589C4—24no—
590C4—42no—
591C4—42no—
592C4—82no—
593C4—444no—
594C4#1062256914yes—
595C4C2×C22⋊C4×D1111yescharacteristic
596C4C2×(C22⋊D11)⋊C411yescharacteristic
597C4C2×#6693611yescharacteristic
598C4C2×#6693711yescharacteristic
599C2—24no—
600C2—82no—
601C2—448no—
602C2C2×#1062256911yescharacteristic
603C2C4×#6700212yes—
604C2#1307784211yescharacteristic
605C2#1307785611yescharacteristic
606C2#1307807612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
cosocleC22×C4×C11C24
hypercenter#2297D11
hypocenterC11#20925
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C22×C4×D44C2semidirect
3. C2×#10622845C2semidirect
4. C2×#10622614C2semidirect
5. #13068967C2semidirect
6. #13068953C2semidirect
7. #13068337C2semidirect
8. #13068310C2semidirect
9. C11×#2297C2semidirect
17. C2×#67002C4semidirect
28. C11×#391C22semidirect
29. C11×#390C22semidirect
34. C2×#66899C22semidirect
35. C2×#66896C22semidirect
38. #10622167C22semidirect
39. #10622162C22semidirect
46. C2×C11×#41C2×C4semidirect
80. C2×#4325C2×C4semidirect
83. C2×#4323C2×C4semidirect
95. C2×#4318C2×C4semidirect
124. C2×Q8×C11C22×C4semidirect
133. C2×D4×C11C22×C4semidirect
165. C2×D44C22⋊C4semidirect
195. C2×C11⋊C8C22×C4semidirect
200. #2297D11semidirect
256. C2×C4×C11AGL(1,ℤ/8)semidirect
297. #391C2×D11semidirect
298. #390C2×D11semidirect
341. C2×#41C4×D11semidirect
426. C2×Q8C2×C4×D11semidirect
448. C2×D4C2×C4×D11semidirect
498. C11#20925semidirect
559. C2×C4#67002semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C22×C4×D442
C2×#106228452
C2×#106226142
#130689672
#130689532
#130683372
#130683102
C11×#22972
#2092511