Finite Group Databasebeta

← #14769416

Subgroups — #14769416

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic
3C2×#10622415C212yesmaximal, complemented
4#13071563C211yesmaximal, characteristic
5#13069539C211yesmaximal, characteristic, complemented
6#13069418C211yesmaximal, characteristic, complemented
7#13069048C212yesmaximal, complemented
8#13068927C212yesmaximal, complemented
9#13068621C211yesmaximal, characteristic, complemented
10#13068549C212yesmaximal, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4313C2212yes—
15Q8×D44—24no—
16Q8×D44C418yescomplemented
17C2×#66950—22no—
18C2×#66950C2212yes—
19C2×#66945C2212yes—
20C2×C4×D44—21no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922—21no—
23C2×#66922C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66880C2212yes—
31C2×#66880C2212yes—
32#10622600C2212yes—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35#10622552—21no—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11—21no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622415—28no—
40#10622301—24no—
41#10622283—22no—
42C11×#340C2211yescharacteristic
43C11×#340C2211yescharacteristic
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C2×Q8×D11—24no—
47C2×Q8×D11—24no—
48C2×Q8×D11—24no—
49C2×Q8×D11—42no—
50C2×Q8×D11—42no—
51C2×Q8×D11C2×C418yes—
52C22×D44D411yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11C2312yes—
55C22×Dic22—22no—
56C22×Dic22C2312yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C4×Q8×C11—22no—
60C4×Q8×C11C2×C414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4D412yes—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C2×C4×Dic11—22no—
80C22×C11⋊C8C2312yes—
81C2×#4313—24no—
82C2×#4313—24no—
83C2×#4313—42no—
84#66950—24no—
85#66950—216no—
86#66950C2×C418yes—
87#66945—24no—
88#66945—42no—
89C4×D44—28no—
90C4×D44C2×C414yes—
91C4×D44D414yes—
92#66922—22no—
93#66922—28no—
94#66922C2×C414yes—
95C11×#103—22no—
96C11×#103D414yescomplemented
97C4×C8×C11—22no—
98C11×#95—21no—
99#66899—24no—
100C11⋊#95—22no—
101(C2×D11)⋊C8—24no—
102#66880—24no—
103#66880—42no—
104#66874—24no—
105#66874—42no—
106C4⋊(C11⋊C8)—22no—
107#22430—111nomaximal, Sylow
108C23×D11C2×D412yes—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11C22×C412yes—
113C2×Q8×C11C2×D412yes—
114C2×Q8×C11#4112yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11C2×D412yes—
125Q8×D11—216no—
126Q8×D11—48no—
127Q8×D11—48no—
128Q8×D11—48no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44C22⋊C414yes—
132C2×C4×D11—28no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—44no—
138C2×C4×D11—44no—
139C2×C4×D11C22×C414yes—
140C2×C4×D11C2×D414yes—
141C2×Dic22—28no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—44no—
148C2×Dic22—44no—
149C2×Dic22C22×C414yes—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C2×D412yes—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4C22×C412yes—
162C11×C4⋊C4C2×D412yes—
163C42×C11—24no—
164C42×C11—42no—
165C42×C11C22×C412yes—
166C42×C11C2×D412yes—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—44no—
169(C2×D11)⋊C4—82no—
170(C2×D11)⋊C4C22⋊C418yes—
171C4⋊Dic11—28no—
172C4⋊Dic11—24no—
173C4⋊Dic11—24no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—42no—
177C4⋊Dic11—81no—
178C4⋊Dic11C22⋊C414yes—
179C4×Dic11—44no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183#4313—48no—
184C2×D4×Q8—111no—
185C2×#436—111no—
186C2×#419—112no—
187#2354—111no—
188#1981—111no—
189#1956—111no—
190#1894—112no—
191#1873—112no—
192#1803—111no—
193#1787—112no—
194C4×#103D1111yescharacteristic, complemented
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11C2×C22⋊C414yes—
203Q8×C11—22no—
204Q8×C11—22no—
205Q8×C11—22no—
206Q8×C11C4×D414yes—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11#13712yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11C2×C22⋊C414yes—
240D44—28no—
241C4×D11—24no—
242C4×D11—24no—
243C4×D11—24no—
244C4×D11—24no—
245C4×D11—416no—
246Dic22—24no—
247Dic22—24no—
248Dic22—416no—
249Dic22—42no—
250Dic22—42no—
251C8×C11—22no—
252C8×C11—41no—
253C11⋊C8—42no—
254C23×Q8—112no—
255C22×M16—112no—
256D4×Q8—118no—
257D4×Q8—224no—
258C2×C4⋊Q8—111no—
259C2×C4⋊Q8—221no—
260C2×C22⋊Q8—112no—
261C2×C22⋊Q8—222no—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×D4—111no—
264C2×C4×D4—221no—
265C2×#117—112no—
266#436—224no—
267C2×C4⋊C8—111no—
268#419—228no—
269C2×#103—112no—
270C2×#103—112no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#103—112no—
274C2×#103C2×D1111yescharacteristic
275C2×#103C2×D1111yescharacteristic
276C2×C22⋊C8—112no—
277C2×C4×C8C2×D1111yescharacteristic
278#390—221no—
279#388—222no—
280#384—111no—
281#380—112no—
282C4×C4⋊C4—221no—
283C4×C4⋊C4C2×D1111yescharacteristic
284#340—112no—
285#340C2×D1111yescharacteristic
286#340C2×D1111yescharacteristic
287C22×C11C22×C22⋊C411yescharacteristic
288C22×C11D4211yescharacteristic
289C22×C11#54611yescharacteristic
290C22×C11C2×#13711yescharacteristic
291C22×C11C2×#13711yescharacteristic
292C22×C11#57711yescharacteristic
293C22×C11#57811yescharacteristic
294C2×D11—24no—
295C2×D11—24no—
296C2×D11—24no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C4×C11—24no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—81no—
306C4×C11#41914yescomplemented
307C4×C11C2×C4×D411yescharacteristic
308C4×C11#51811yescharacteristic
309C4×C11D4211yescharacteristic
310C4×C11#54611yescharacteristic
311Dic11—24no—
312Dic11—44no—
313Dic11—82no—
314C22×Q8—118no—
315C22×Q8—112no—
316C22×Q8—222no—
317C22×Q8—224no—
318C22×Q8—224no—
319C22×Q8—224no—
320C22×Q8—442no—
321C22×Q8—442no—
322C22×Q8C22×D1111yescharacteristic
323C22×D4—111no—
324C23×C4—112no—
325C23×C4—222no—
326C2×M16—224no—
327C2×M16—224no—
328C2×M16—442no—
329C22×C8—112no—
330C22×C8C22×D1111yescharacteristic
331C22×C8C22×D1111yescharacteristic
332C4⋊Q8—114no—
333C4⋊Q8—228no—
334C4⋊Q8—222no—
335C22⋊Q8—118no—
336C22⋊Q8—2216no—
337C22⋊Q8—224no—
338C4×Q8—22no—
339C4×Q8C4×D1114yes—
340C4×D4—114no—
341C4×D4—114no—
342C4×D4—228no—
343#117—224no—
344#117—442no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C4⋊C4C22×D1111yescharacteristic
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C22⋊C4—112no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—222no—
363C2×C42C22×D1111yescharacteristic
364C4⋊C8—222no—
365#103—22no—
366#103—224no—
367#103—224no—
368#103—224no—
369#103—442no—
370#103—442no—
371#103D4414yescomplemented
372C22⋊C8—224no—
373C4×C8—22no—
374#95—21no—
375#95—222no—
376C2×C11D4×C22⋊C411yescharacteristic
377C2×C11C2×#41911yescharacteristic
378C2×C11#289811yescharacteristic
379C2×C11#327611yescharacteristic
380C2×C11#327811yescharacteristic
381C2×C11#332811yescharacteristic
382C2×C11#332911yescharacteristic
383D11—44no—
384C24—112no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—114no—
389C2×Q8—228no—
390C2×Q8—222no—
391C2×Q8—2216no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—444no—
397C2×Q8—444no—
398C2×Q8—448no—
399C2×Q8—448no—
400C2×Q8—448no—
401C2×Q8C2×C4×D1112yes—
402C2×Q8C2×D4412yes—
403C2×Q8#433912yes—
404C2×D4—114no—
405C2×D4—222no—
406C2×D4—222no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—112no—
412C22×C4—114no—
413C22×C4—114no—
414C22×C4—228no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—444no—
422C22×C4—444no—
423C22×C4D4×D1111yescharacteristic
424C22×C4D4×D1111yescharacteristic
425C22×C4C23×D1111yescharacteristic
426M16—448no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8C2×D4412yes—
436C4⋊C4—24no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—114no—
442C4⋊C4—228no—
443C4⋊C4—224no—
444C4⋊C4—224no—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4—442no—
448C4⋊C4—881no—
449C4⋊C4C2×C4×D1112yes—
450C4⋊C4C2×D4412yes—
451C22⋊C4—118no—
452C22⋊C4—228no—
453C22⋊C4—444no—
454C22⋊C4—882no—
455C42—24no—
456C42—42no—
457C42—444no—
458C42C2×C4×D1112yes—
459C42D4×D1112yes—
460C11#2243011yescharacteristic, complemented, Sylow
461C23—114no—
462C23—222no—
463C23—222no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23C2×D4×D1111yescharacteristic
469Q8—22no—
470Q8—22no—
471Q8—22no—
472Q8—224no—
473Q8—224no—
474Q8—4416no—
475Q8—442no—
476Q8—442no—
477Q8C4×D4414yes—
478D4—228no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—114no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—4416no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4C22⋊C4×D1112yes—
508C2×C4C22⋊C4×D1112yes—
509C2×C4#6696812yes—
510C2×C4#6697112yes—
511C2×C4C22×C4×D1111yescharacteristic
512C2×C4C22×D4411yescharacteristic
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4#6704211yescharacteristic
516C2×C4#6704211yescharacteristic
517C8—22no—
518C8—41no—
519C8—442no—
520C22—224no—
521C22—224no—
522C22—224no—
523C22—442no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22C2×C22⋊C4×D1111yescharacteristic
528C22D4×D4411yescharacteristic
529C22#1062308111yescharacteristic
530C22C2×#6696811yescharacteristic
531C22C2×#6697111yescharacteristic
532C22#1062330111yescharacteristic
533C22#1062330211yescharacteristic
534C4—24no—
535C4—22no—
536C4—42no—
537C4—42no—
538C4—81no—
539C4—224no—
540C4—444no—
541C4—882no—
542C4#1062241514yescomplemented
543C4C2×C4×D4411yescharacteristic
544C4#1062305211yescharacteristic
545C4D4×D4411yescharacteristic
546C4#1062308111yescharacteristic
547C2—444no—
548C2C22⋊C4×D4411yescharacteristic
549C2C2×#1062241511yescharacteristic
550C2#1307714511yescharacteristic
551C2#1308026311yescharacteristic
552C2#1308028311yescharacteristic
553C2#1308090111yescharacteristic
554C2#1308091211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenterC4×#103D11
hypocenterC11#22430
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
3. C2×#10622415C2semidirect
5. #13069539C2semidirect
6. #13069418C2semidirect
7. #13069048C2semidirect
8. #13068927C2semidirect
9. #13068621C2semidirect
10. #13068549C2semidirect
11. C4×C11×#103C2semidirect
16. Q8×D44C4semidirect
96. C11×#103D4semidirect
194. C4×#103D11semidirect
306. C4×C11#419semidirect
371. #103D44semidirect
460. C11#22430semidirect
542. C4#10622415semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D442
C2×#106223012
C2×#106224152
#130715632
#130695392
#130694182
#130690482
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C4×C11×#1032
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