Finite Group Databasebeta

← #14804488

Subgroups — #14804488

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622728C212yesmaximal, complemented
2C2×#10622456C211yesmaximal, characteristic, complemented
3#13073562C211yesmaximal, characteristic, complemented
4#13073529C211yesmaximal, characteristic, complemented
5#13069799C212yesmaximal, complemented
6#13069614C212yesmaximal, complemented
7#13069422C211yesmaximal, characteristic, complemented
8#13069375C211yesmaximal, characteristic, complemented
9#13069044C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C8×D4×C11C211yesmaximal, characteristic, complemented
12C23×C8×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66993—21no—
15C2×#66991—21no—
16C2×#66983C2212yes—
17C2×#66983C2212yes—
18C2×#66983C2212yes—
19C22×D88C2212yes—
20C2×#66927C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C8×D4×C11—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26#10622825C2212yes—
27#10622728—28no—
28C2×#66885C2212yes—
29C2×#66885C2211yescharacteristic
30C2×#66885C2212yes—
31C2×#66885C2212yes—
32C2×#66885C2211yescharacteristic
33C2×#66882C2212yes—
34#10622601—21no—
35#10622600—21no—
36#10622574—22no—
37#10622573—22no—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622456—24no—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×C22⋊D11—22no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44C2312yes—
52C22×D44C2311yescharacteristic
53C22×C4×D11—21no—
54C22×C8×C11—24no—
55C22×C8×C11—24no—
56C22×C8×C11—42no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4D412yes—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66#66993—44no—
67#66991—44no—
68#66983—24no—
69#66983—24no—
70#66983—24no—
71#66983—42no—
72#66983—42no—
73#66983—42no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4×Dic11—21no—
85C2×D88—24no—
86C2×D88—24no—
87C2×D88—42no—
88#66927—22no—
89#66927—22no—
90C4×D44—22no—
91C4×D44—22no—
92C11×C4⋊C8D414yescomplemented
93C11×C22⋊C8—24no—
94C4×C8×C11—22no—
95C11⋊#95—21no—
96C11⋊#95—22no—
97#66885—24no—
98#66885—24no—
99#66885—22no—
100#66885—42no—
101#66885D414yescomplemented
102#66882—24no—
103#25384—111nomaximal, Sylow
104C24×C11C2×D412yes—
105C23×D11—21no—
106C23×D11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11D814yescomplemented
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C2×C22⋊D11—44no—
121C2×C22⋊D11—44no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—44no—
124C2×C22⋊D11—44no—
125C2×C22⋊D11—44no—
126C2×C22⋊D11—82no—
127C2×C22⋊D11—82no—
128C2×C22⋊D11—82no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C2×D44—21no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—42no—
145C2×D44—42no—
146C2×D44—42no—
147C2×D44—42no—
148C2×D44—81no—
149C2×D44—81no—
150C2×D44C2×D412yes—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—48no—
162C2×C8×C11C2×D412yes—
163C2×C8×C11C2×D414yes—
164C11×C4⋊C4—22no—
165C11×C22⋊C4—24no—
166C42×C11C2×D412yes—
167C42×C11#4112yes—
168C22⋊Dic11—44no—
169(C2×D11)⋊C4—44no—
170(C2×D11)⋊C4—44no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—42no—
173C4⋊Dic11—22no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C4⋊Dic11—81no—
181C4⋊Dic11C2×D412yes—
182C4⋊Dic11#4112yes—
183C4×Dic11—42no—
184D88—48no—
185C2×#466—112no—
186C2×#459—111no—
187C2×C8×D4D1111yescharacteristic, complemented
188#2541—111no—
189#2537—111no—
190#2033—112no—
191#1999—112no—
192#1957—111no—
193#1947—111no—
194#1893—112no—
195C4×#102—111no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11C2×D814yes—
203C23×C11C22×D411yescharacteristic
204C22×D11—22no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218D4×C11—28no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11#12112yes—
229C2×C4×C11#12112yes—
230C2×C4×C11C2×D812yes—
231C2×C4×C11#13512yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C22⋊D11—88no—
239C22⋊D11—88no—
240C22⋊D11—88no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—42no—
253D44—22no—
254D44—22no—
255D44—42no—
256D44—41no—
257D44—42no—
258D44—42no—
259D44—41no—
260D44—42no—
261D44—84no—
262D44—84no—
263C4×D11—84no—
264C8×C11—24no—
265C8×C11—22no—
266C8×C11—41no—
267C22×D8—112no—
268C23×C8C2×D1112yes—
269C2×#127—111no—
270C2×#127—221no—
271C2×#121—112no—
272C2×#121—112no—
273C2×#121—112no—
274C2×#121—221no—
275C2×C4×D4—111no—
276C2×C4×D4C2×D1111yescharacteristic
277#466—228no—
278#459—224no—
279C8×D4—24no—
280C2×#107—112no—
281C2×C4⋊C8C2×D1111yescharacteristic
282C2×#102—111no—
283C2×#102—112no—
284C2×#102—112no—
285C2×#102—111no—
286C2×#102—112no—
287C2×C22⋊C8C2×D1112yes—
288C2×C4×C8C2×D1111yescharacteristic
289#394—222no—
290#392—222no—
291#390—221no—
292#384—111no—
293#380—112no—
294#380—221no—
295C4×C4⋊C4—111no—
296#340—111no—
297#340—112no—
298#340—111no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11C2×#12111yescharacteristic
307C22×C11D4211yescharacteristic
308C22×C11#54611yescharacteristic
309C22×C11C22×D811yescharacteristic
310C22×C11C2×#13511yescharacteristic
311C22×C11#57611yescharacteristic
312C22×C11#57711yescharacteristic
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—82no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C2×D11—82no—
327C4×C11—22no—
328C4×C11—42no—
329C4×C11#46614yescomplemented
330C4×C11#53211yescharacteristic
331C4×C11#54011yescharacteristic
332C4×C11D4211yescharacteristic
333C4×C11#55011yescharacteristic
334Dic11—42no—
335Dic11—42no—
336Dic11—82no—
337Dic11—81no—
338C22×D4—111no—
339C22×D4—112no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—221no—
344C22×D4—221no—
345C22×D4D4411yescharacteristic
346C23×C4—221no—
347C23×C4C22×D1112yes—
348C2×D8—224no—
349C2×D8—224no—
350C2×D8—442no—
351C22×C8—24no—
352C22×C8—24no—
353C22×C8—42no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1112yes—
357#127—222no—
358#127—222no—
359#127—444no—
360#121—224no—
361#121—224no—
362#121—224no—
363#121—442no—
364#121—442no—
365#121—442no—
366#121—444no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—222no—
370C4×D4—222no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4D4411yescharacteristic
378C2×C22⋊C4—222no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4D4412yes—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—224no—
387C4⋊C8C22⋊D1114yescomplemented
388#102—114no—
389#102—222no—
390#102—224no—
391#102—224no—
392#102—442no—
393C22⋊C8—24no—
394C4×C8—22no—
395#95—221no—
396#95—222no—
397C2×C11—44no—
398C2×C11#242811yescharacteristic
399C2×C11C2×#46611yescharacteristic
400C2×C11#306211yescharacteristic
401C2×C11D4×D811yescharacteristic
402C2×C11#328411yescharacteristic
403C2×C11#329411yescharacteristic
404C2×C11#330511yescharacteristic
405D11—82no—
406D11—162no—
407C24—221no—
408C24—222no—
409C24C2×D4412yes—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—112no—
413C2×D4—221no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—221no—
417C2×D4—222no—
418C2×D4—221no—
419C2×D4—222no—
420C2×D4—221no—
421C2×D4—222no—
422C2×D4—221no—
423C2×D4—222no—
424C2×D4—444no—
425C2×D4—444no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—442no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4—442no—
434C2×D4—881no—
435C2×D4—881no—
436C2×D4—882no—
437C2×D4—882no—
438C2×D4—882no—
439C2×D4D8814yescomplemented
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—222no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4C2×D4412yes—
454C22×C4C2×D4411yescharacteristic
455C22×C4C2×D4411yescharacteristic
456C22×C4C23×D1111yescharacteristic
457D8—448no—
458C2×C8—22no—
459C2×C8—21no—
460C2×C8—22no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—48no—
466C2×C8D4×D1112yes—
467C2×C8C2×C22⋊D1114yes—
468C4⋊C4—22no—
469C4⋊C4—112no—
470C4⋊C4—112no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—222no—
475C4⋊C4—222no—
476C4⋊C4—221no—
477C4⋊C4—442no—
478C4⋊C4—881no—
479C22⋊C4—24no—
480C22⋊C4—444no—
481C22⋊C4—444no—
482C22⋊C4—444no—
483C22⋊C4—444no—
484C22⋊C4—442no—
485C42—442no—
486C42#433912yes—
487C42C2×C22⋊D1112yes—
488C11#2538411yescharacteristic, complemented, Sylow
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—222no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23—441no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23C2×D8814yes—
510C23C22×D4411yescharacteristic
511D4—28no—
512D4—222no—
513D4—222no—
514D4—442no—
515D4—442no—
516D4—441no—
517D4—442no—
518D4—441no—
519D4—442no—
520D4—884no—
521D4—888no—
522D4—888no—
523D4—888no—
524D4—884no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—442no—
542C2×C4—441no—
543C2×C4—442no—
544C2×C4—441no—
545C2×C4—442no—
546C2×C4—884no—
547C2×C4C2×D8812yes—
548C2×C4#6695712yes—
549C2×C4#6698312yes—
550C2×C4#6698312yes—
551C2×C4C2×#433911yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#6704211yescharacteristic
556C2×C4C22×C22⋊D1111yescharacteristic
557C8—22no—
558C8—24no—
559C8—41no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—442no—
568C22—442no—
569C22—442no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22—881no—
574C22—882no—
575C22—882no—
576C22—882no—
577C22—882no—
578C22—882no—
579C22—882no—
580C22—882no—
581C22D4×D4411yescharacteristic
582C22#1062308511yescharacteristic
583C22C22×D8811yescharacteristic
584C22C2×#6695711yescharacteristic
585C22#1062328211yescharacteristic
586C22#1062328311yescharacteristic
587C22C2×#6698311yescharacteristic
588C4—22no—
589C4—42no—
590C4—442no—
591C4—442no—
592C4—881no—
593C4—882no—
594C4#1062272814yescomplemented
595C4#1062307911yescharacteristic
596C4#1062309311yescharacteristic
597C4D4×C22⋊D1111yescharacteristic
598C4#1062336511yescharacteristic
599C2—44no—
600C2—882no—
601C2—1762no—
602C2#1307219811yescharacteristic
603C2C2×#1062272811yescharacteristic
604C2#1307829611yescharacteristic
605C2D4×D8811yescharacteristic
606C2#1308034811yescharacteristic
607C2#1308043011yescharacteristic
608C2#1308056711yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11C22×D4
hypercenterC2×C8×D4D11
hypocenterC11#25384
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622728C2semidirect
2. C2×#10622456C2semidirect
3. #13073562C2semidirect
4. #13073529C2semidirect
5. #13069799C2semidirect
6. #13069614C2semidirect
7. #13069422C2semidirect
8. #13069375C2semidirect
9. #13069044C2semidirect
10. C4×#66885C2semidirect
11. C2×C8×D4×C11C2semidirect
92. C11×C4⋊C8D4semidirect
101. #66885D4semidirect
109. C2×D4×C11D8semidirect
187. C2×C8×D4D11semidirect
329. C4×C11#466semidirect
387. C4⋊C8C22⋊D11semidirect
439. C2×D4D88semidirect
488. C11#25384semidirect
594. C4#10622728semidirect

Maximal subgroups

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

subgroupindex
C2×#106227282
C2×#106224562
#130735622
#130735292
#130697992
#130696142
#130694222
#130693752
#130690442
C4×#668852
C2×C8×D4×C112
#2538411