Finite Group Databasebeta

← #14804494

Subgroups — #14804494

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×#10622388C212yesmaximal, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic, complemented
4#13073558C211yesmaximal, characteristic, complemented
5#13073529C211yesmaximal, characteristic, complemented
6#13069801C212yesmaximal, complemented
7#13069613C212yesmaximal, complemented
8#13069422C211yesmaximal, characteristic, complemented
9#13069374C211yesmaximal, characteristic, complemented
10#13069043C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66991C2212yes—
14C22×#4323C2212yes—
15C2×#66983—21no—
16C22×C8×D11C2212yes—
17C2×#66948C2212yes—
18C2×#66948C2212yes—
19C2×#66927—21no—
20C2×#66927C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622825—21no—
27C2×#66885C2212yes—
28C2×#66885C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30#10622628—24no—
31#10622600C2212yes—
32C2×#66873C2212yes—
33C2×#66871C2212yes—
34#10622574—22no—
35#10622552—21no—
36#10622548C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622388—28no—
39C8×D44—24no—
40#10622284—22no—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×C22⋊D11—22no—
47C22×D44—21no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—21no—
51C22×D44D411yescharacteristic
52C22×D44C2312yes—
53C22×C4×D11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65#66991—24no—
66#66991—42no—
67C2×#4323—24no—
68C2×#4323—24no—
69C2×#4323—42no—
70#66983—44no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D412yes—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80C2×C8×D11—24no—
81C2×C8×D11—24no—
82C2×C8×D11—42no—
83#66948—24no—
84#66948—24no—
85#66948—42no—
86#66948—42no—
87#66927—22no—
88#66927—22no—
89#66927—44no—
90C4×D44—22no—
91C4×D44—22no—
92C11×#102—22no—
93C11×#102D414yescomplemented
94C4×C8×C11—22no—
95C11×#95—21no—
96C11⋊#95—22no—
97#66885—24no—
98#66885—42no—
99(C2×D11)⋊C8—24no—
100#66873—24no—
101#66871—24no—
102C4⋊(C11⋊C8)D414yescomplemented
103#25384—111nomaximal, Sylow
104C24×C11—21no—
105C23×D11—22no—
106C23×D11C2×D412yes—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11C2×D412yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—44no—
123C2×C22⋊D11—44no—
124C2×C22⋊D11—82no—
125C22×Dic11—22no—
126C22×Dic11C2×D412yes—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—44no—
136C2×D44—44no—
137C2×D44—44no—
138C2×D44—44no—
139C2×D44—42no—
140C2×D44—42no—
141C2×D44—42no—
142C2×D44—42no—
143C2×D44—81no—
144C2×D44—81no—
145C2×D44—82no—
146C2×D44—82no—
147C2×D44D814yescomplemented
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C2×D412yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4#4112yes—
166C11×C22⋊C4—42no—
167C42×C11—42no—
168C42×C11C2×D412yes—
169C42×C11#4112yes—
170C22⋊Dic11—44no—
171#4323—48no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—44no—
175(C2×D11)⋊C4—44no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C4⋊Dic11—81no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8C2×D414yes—
184C8×D11—48no—
185C2×#466—112no—
186C2×#459—111no—
187C2×C8×D4—111no—
188#2541—111no—
189#2537—111no—
190#2033—112no—
191#1999—112no—
192#1957—111no—
193#1947—111no—
194#1893—112no—
195C4×#102D1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11C22×D411yescharacteristic
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11C2×D814yes—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—41no—
221D4×C11—41no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—84no—
234C2×C4×C11#12112yes—
235C2×C4×C11#12112yes—
236C2×C4×C11C2×D812yes—
237C2×C4×C11#13512yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C22⋊D11—88no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251D44—28no—
252D44—42no—
253D44—42no—
254D44—42no—
255D44—42no—
256D44—84no—
257D44—88no—
258D44—88no—
259D44—84no—
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—42no—
263C4×D11—42no—
264C8×C11—22no—
265C8×C11—41no—
266C11⋊C8—24no—
267C22×D8—112no—
268C23×C8—112no—
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—224no—
280C2×#107—112no—
281C2×C4⋊C8—111no—
282C2×#102—112no—
283C2×#102—112no—
284C2×#102—112no—
285C2×#102C2×D1111yescharacteristic
286C2×#102C2×D1111yescharacteristic
287C2×C22⋊C8—112no—
288C2×C4×C8C2×D1111yescharacteristic
289#394—222no—
290#392—222no—
291#390—221no—
292#384—111no—
293#380—112no—
294#380—221no—
295C4×C4⋊C4C2×D1111yescharacteristic
296#340—112no—
297#340C2×D1111yescharacteristic
298#340C2×D1111yescharacteristic
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11C2×#12111yescharacteristic
307C22×C11D4211yescharacteristic
308C22×C11#54611yescharacteristic
309C22×C11C22×D811yescharacteristic
310C22×C11C2×#13511yescharacteristic
311C22×C11#57611yescharacteristic
312C22×C11#57711yescharacteristic
313C2×D11—24no—
314C2×D11—24no—
315C2×D11—24no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—42no—
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—42no—
330C4×C11—81no—
331C4×C11#46614yescomplemented
332C4×C11#53211yescharacteristic
333C4×C11#54011yescharacteristic
334C4×C11D4211yescharacteristic
335C4×C11#55011yescharacteristic
336Dic11—42no—
337Dic11—82no—
338C22×D4—111no—
339C22×D4—112no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—221no—
344C22×D4—221no—
345C22×D4C22×D1111yescharacteristic
346C23×C4—21no—
347C23×C4—112no—
348C2×D8—224no—
349C2×D8—224no—
350C2×D8—442no—
351C22×C8—112no—
352C22×C8—224no—
353C22×C8—224no—
354C22×C8—442no—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
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—112no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—112no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C42—21no—
385C2×C42C22×D1111yescharacteristic
386#107—224no—
387C4⋊C8—114no—
388#102—22no—
389#102—224no—
390#102—224no—
391#102—442no—
392#102D4414yescomplemented
393C22⋊C8—224no—
394C4×C8—22no—
395#95—21no—
396#95—222no—
397C2×C11—82no—
398C2×C11#242811yescharacteristic
399C2×C11C2×#46611yescharacteristic
400C2×C11#306211yescharacteristic
401C2×C11D4×D811yescharacteristic
402C2×C11#328411yescharacteristic
403C2×C11#329411yescharacteristic
404C2×C11#330511yescharacteristic
405D11—44no—
406D11—162no—
407C24—21no—
408C24—112no—
409C24—222no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—114no—
416C2×D4—222no—
417C2×D4—222no—
418C2×D4—222no—
419C2×D4—222no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—222no—
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×D4C2×D4412yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—112no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457D8—448no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—114no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—448no—
467C2×C8C2×D4412yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—222no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4—442no—
476C4⋊C4—881no—
477C4⋊C4C2×D4412yes—
478C4⋊C4#433912yes—
479C22⋊C4—42no—
480C22⋊C4—224no—
481C22⋊C4—444no—
482C22⋊C4—444no—
483C22⋊C4—444no—
484C22⋊C4—444no—
485C42—42no—
486C42#433912yes—
487C42D4×D1112yes—
488C11#2538411yescharacteristic, complemented, Sylow
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—114no—
497C23—222no—
498C23—222no—
499C23—222no—
500C23—222no—
501C23—222no—
502C23—222no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23C2×D4×D1111yescharacteristic
511D4—22no—
512D4—22no—
513D4—41no—
514D4—41no—
515D4—228no—
516D4—442no—
517D4—442no—
518D4—442no—
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—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—84no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4#6693712yes—
548C2×C4#6693712yes—
549C2×C4D8×D1112yes—
550C2×C4#6696912yes—
551C2×C4C22×D4411yescharacteristic
552C2×C4C2×#433911yescharacteristic
553C2×C4C2×#433911yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#6704211yescharacteristic
556C2×C4#6704211yescharacteristic
557C8—22no—
558C8—41no—
559C8—224no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—224no—
568C22—224no—
569C22—224no—
570C22—442no—
571C22—442no—
572C22—442no—
573C22—442no—
574C22—882no—
575C22—882no—
576C22—882no—
577C22—882no—
578C22—882no—
579C22—882no—
580C22—882no—
581C22C2×#6693711yescharacteristic
582C22D4×D4411yescharacteristic
583C22#1062308111yescharacteristic
584C22C2×D8×D1111yescharacteristic
585C22C2×#6696911yescharacteristic
586C22#1062330011yescharacteristic
587C22#1062330111yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—81no—
592C4—442no—
593C4—882no—
594C4#1062238814yescomplemented
595C4#1062300811yescharacteristic
596C4#1062306611yescharacteristic
597C4D4×D4411yescharacteristic
598C4#1062308411yescharacteristic
599C2—82no—
600C2—444no—
601C2—1762no—
602C2#1307220411yescharacteristic
603C2C2×#1062238811yescharacteristic
604C2#1307829911yescharacteristic
605C2D8×D4411yescharacteristic
606C2#1308034711yescharacteristic
607C2#1308043111yescharacteristic
608C2#1308056811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
hypercenterC4×#102D11
hypocenterC11#25384
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10622388C2semidirect
2. C2×#10622628C2semidirect
3. C2×C8×D44C2semidirect
4. #13073558C2semidirect
5. #13073529C2semidirect
6. #13069801C2semidirect
7. #13069613C2semidirect
8. #13069422C2semidirect
9. #13069374C2semidirect
10. #13069043C2semidirect
11. C4×C11×#102C2semidirect
93. C11×#102D4semidirect
102. C4⋊(C11⋊C8)D4semidirect
147. C2×D44D8semidirect
195. C4×#102D11semidirect
331. C4×C11#466semidirect
392. #102D44semidirect
488. C11#25384semidirect
594. C4#10622388semidirect

Maximal subgroups

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

subgroupindex
C2×#106223882
C2×#106226282
C2×C8×D442
#130735582
#130735292
#130698012
#130696132
#130694222
#130693742
#130690432
C4×C11×#1022
#2538411