Finite Group Databasebeta

← #14788125

Subgroups — #14788125

Order 2816.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2C2×#10622464C211yesmaximal, characteristic, complemented
3C2×#10622461C211yesmaximal, characteristic, complemented
4C4×#66977C211yesmaximal, characteristic, complemented
5#13069806C212yesmaximal, complemented
6#13069621C212yesmaximal, complemented
7#13069567C211yesmaximal, characteristic, complemented
8#13069542C211yesmaximal, characteristic, complemented
9#13068949C212yesmaximal, complemented
10#13068880C212yesmaximal, complemented
11C11×#1797C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C22×C42×C11C2211yescharacteristic
14C2×#66983—21no—
15C2×#66983C2212yes—
16C2×#66977C2211yescharacteristic
17C22×#4314C2212yes—
18#10623008—24no—
19#10623008—24no—
20C2×#66928—21no—
21C2×#66927C2211yescharacteristic
22C2×C4×D44—21no—
23C2×C4×D44C2212yes—
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2212yes—
29#10622825C2211yescharacteristic
30#10622823—21no—
31C4×C22⋊Dic11—21no—
32C2×#66885C2212yes—
33C2×#66885C2212yes—
34C2×#66885C2212yes—
35C2×#66881C2212yes—
36C2×#66880C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38#10622546—21no—
39C4×Dic11⋊C4—21no—
40#10622542C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622464—24no—
43#10622461—24no—
44C11×#336C2212yes—
45#10622189C2212yes—
46#10622189C2212yes—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—22no—
51C2×#4339—28no—
52C2×#4339—44no—
53C2×#4339—44no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44C2312yes—
57C22×C4×D11—22no—
58C22×Dic22—21no—
59C22×Dic22C2311yescharacteristic
60C22×C8×C11C2312yes—
61C22×C8×C11C2312yes—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11D411yescharacteristic
65C2×C42×C11D411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70#66983—28no—
71#66983—24no—
72#66983—24no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C2×C4⋊Dic11C2311yescharacteristic
80#66977—22no—
81#66977—22no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×#4314—24no—
88C2×#4314—24no—
89C2×#4314—42no—
90#66928—28no—
91#66927—22no—
92#66927D414yes—
93C4×D44—28no—
94C4×D44—24no—
95C4×D44—24no—
96#66922—22no—
97#66922D414yes—
98C4×Dic22—22no—
99C4×Dic22—22no—
100C11×C4⋊C8—22no—
101C11×C4⋊C8—22no—
102C11×C22⋊C8—42no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108#66885—24no—
109#66885—24no—
110#66885—42no—
111#66881—24no—
112#66880—24no—
113#24154—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C23×D11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11SD1614yescomplemented
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—28no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142#4339—432no—
143C2×D44—24no—
144C2×D44—24no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44C2×D414yes—
155C2×C4×D11—28no—
156C2×C4×D11—44no—
157C2×C4×D11—44no—
158C2×Dic22—24no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—42no—
165C2×Dic22—42no—
166C2×Dic22#4112yescomplemented
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11C2×D412yes—
178C42×C11C2×D412yes—
179C22⋊Dic11—24no—
180C22⋊Dic11—42no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—28no—
183C4⋊Dic11—24no—
184C4⋊Dic11—22no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2×D414yes—
191C4⋊Dic11#4112yescomplemented
192Dic11⋊C4—24no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197#4314—48no—
198C2×#532—111no—
199C2×#475—111no—
200C2×#460—111no—
201C4×C22⋊Q8—111no—
202#2034—112no—
203#2000—112no—
204#1988—111no—
205#1982—111no—
206#1877—112no—
207#1864—112no—
208#1797D1111yescharacteristic, complemented
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11C2×SD1612yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—24no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—28no—
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—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11#12012yes—
241C2×C4×C11#12012yes—
242C2×C4×C11C2×SD1612yes—
243C2×C4×C11C2×SD1612yes—
244C2×C4×C11AGL(1,ℤ/8)12yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C22⋊D11—416no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—42no—
258C2×Dic11—41no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267D44—24no—
268D44—24no—
269D44—48no—
270D44—42no—
271D44—42no—
272D44—48no—
273C4×D11—416no—
274Dic22—22no—
275Dic22—22no—
276Dic22—41no—
277Dic22—41no—
278Dic22—48no—
279C8×C11—42no—
280C8×C11—42no—
281C22×#41—221no—
282C22×SD16—112no—
283#532—224no—
284#532—224no—
285C2×C4⋊Q8—111no—
286C2×#127—111no—
287C2×#124—221no—
288C2×C22⋊Q8—111no—
289C2×#121—112no—
290C2×#121—221no—
291C2×C4×Q8—111no—
292C2×C4×D4—112no—
293C2×C4×D4—221no—
294C22×C42C2×D1111yescharacteristic
295#475—224no—
296#460—224no—
297C2×#106—112no—
298C2×C4⋊C8C2×D1111yescharacteristic
299C2×C4⋊C8C2×D1111yescharacteristic
300C2×#103—112no—
301C2×#102—112no—
302C2×#102—112no—
303C2×#102—112no—
304C2×C22⋊C8C2×D1112yes—
305#391—111no—
306#389—111no—
307#387—221no—
308#385—221no—
309#380—111no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—221no—
312C4×C22⋊C4—221no—
313#340—112no—
314#340—112no—
315#336C2×D1112yes—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11C2×#12011yescharacteristic
324C22×C11#52511yescharacteristic
325C22×C11#53711yescharacteristic
326C22×C11C22×SD1611yescharacteristic
327C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C11#57511yescharacteristic
329C22×C11#57511yescharacteristic
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—82no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11#45014yes—
342C4×C11#54611yescharacteristic
343C4×C11#54711yescharacteristic
344C4×C11#54811yescharacteristic
345C4×C11#55011yescharacteristic
346Dic11—42no—
347Dic11—42no—
348Dic11—44no—
349Dic11—81no—
350Dic11—81no—
351C2×#41—228no—
352C2×#41—444no—
353C2×#41—444no—
354C22×Q8—111no—
355C22×Q8—221no—
356C22×D4—112no—
357C22×D4—222no—
358C22×D4—221no—
359C22×D4—221no—
360C23×C4—222no—
361C23×C4D4411yescharacteristic
362C23×C4D4411yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×SD16—224no—
365C2×SD16—224no—
366C2×SD16—442no—
367C22×C8C22×D1112yes—
368C22×C8C22×D1112yes—
369C4⋊Q8—114no—
370C4⋊Q8—222no—
371#127—114no—
372#127—222no—
373#124—228no—
374C22⋊Q8—222no—
375C22⋊Q8—222no—
376#121—224no—
377#121—224no—
378#121—228no—
379C4×Q8—222no—
380C4×Q8—222no—
381C4×D4—224no—
382C4×D4—224no—
383C4×D4—228no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—221no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42D4411yescharacteristic
401C2×C42D4411yescharacteristic
402C2×C42C22×D1111yescharacteristic
403C2×C42C22×D1111yescharacteristic
404#106—224no—
405C4⋊C8—22no—
406C4⋊C8—22no—
407#103—224no—
408#102—224no—
409#102—224no—
410#102—442no—
411C22⋊C8—42no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417C2×C11—42no—
418C2×C11#240711yescharacteristic
419C2×C11C2×#45011yescharacteristic
420C2×C11#300511yescharacteristic
421C2×C11#310311yescharacteristic
422C2×C11#311511yescharacteristic
423C2×C11#324611yescharacteristic
424C2×C11#325111yescharacteristic
425D11—84no—
426C24—222no—
427C24C2×D4411yescharacteristic
428#41—4432no—
429C2×Q8—112no—
430C2×Q8—224no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—442no—
437C2×Q8—442no—
438C2×D4—114no—
439C2×D4—228no—
440C2×D4—224no—
441C2×D4—224no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—442no—
448C2×D4—442no—
449C2×D4—444no—
450C2×D4—444no—
451C2×D4—442no—
452C2×D4—442no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—228no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—444no—
471C22×C4—444no—
472C22×C4#431414yescomplemented
473C22×C4C2×D4411yescharacteristic
474C22×C4C2×D4411yescharacteristic
475C22×C4C2×D4411yescharacteristic
476C22×C4C2×D4411yescharacteristic
477C22×C4C2×D4411yescharacteristic
478C22×C4C23×D1111yescharacteristic
479SD16—448no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C4⋊C4—114no—
487C4⋊C4—112no—
488C4⋊C4—224no—
489C4⋊C4—224no—
490C4⋊C4—222no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C22⋊C4—228no—
499C22⋊C4—228no—
500C22⋊C4—224no—
501C22⋊C4—442no—
502C42—22no—
503C42—22no—
504C42—21no—
505C42—21no—
506C42—442no—
507C42—442no—
508C42D4×D1112yes—
509C42D4×D1112yes—
510C11#2415411yescharacteristic, complemented, Sylow
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—224no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23C2×#431412yes—
525C23C22×D4411yescharacteristic
526Q8—222no—
527Q8—222no—
528Q8—448no—
529Q8—441no—
530Q8—441no—
531D4—224no—
532D4—224no—
533D4—448no—
534D4—4416no—
535D4—448no—
536D4—442no—
537D4—442no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—28no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—224no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—4416no—
558C2×C4—442no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—442no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4#6693512yes—
571C2×C4#6693512yes—
572C2×C4C2×#431412yes—
573C2×C4C2×#431412yes—
574C2×C4#6696112yes—
575C2×C4C2×D4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4#6703711yescharacteristic
578C2×C4#6704011yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C8—42no—
582C8—42no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—882no—
594C22—882no—
595C22—882no—
596C22—882no—
597C22C2×#6693511yescharacteristic
598C22#1062304111yescharacteristic
599C22#1062305511yescharacteristic
600C22C22×#431411yescharacteristic
601C22C2×#6696111yescharacteristic
602C22#1062327911yescharacteristic
603C22#1062327911yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—444no—
609C4—442no—
610C4—442no—
611C4—881no—
612C4—881no—
613C4#1062234414yes—
614C4#1062313011yescharacteristic
615C4#1062314311yescharacteristic
616C4#1062316211yescharacteristic
617C4#1062316411yescharacteristic
618C2—42no—
619C2—884no—
620C2#1307196211yescharacteristic
621C2C2×#1062234411yescharacteristic
622C2#1307786111yescharacteristic
623C2#1307864811yescharacteristic
624C2#1307876811yescharacteristic
625C2#1307993311yescharacteristic
626C2#1307997911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1797C2
socleC23×C11C22×D4
prime radicalC2×#10623008C2
hypercenter#1797D11
hypocenterC11#24154
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#10622464C2semidirect
3. C2×#10622461C2semidirect
4. C4×#66977C2semidirect
5. #13069806C2semidirect
6. #13069621C2semidirect
7. #13069567C2semidirect
8. #13069542C2semidirect
9. #13068949C2semidirect
10. #13068880C2semidirect
11. C11×#1797C2semidirect
127. C22×C4×C11SD16semidirect
166. C2×Dic22#41semidirect
191. C4⋊Dic11#41semidirect
208. #1797D11semidirect
472. C22×C4#4314semidirect
510. C11#24154semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106224642
C2×#106224612
C4×#669772
#130698062
#130696212
#130695672
#130695422
#130689492
#130688802
C11×#17972
#2415411