Finite Group Databasebeta

← #14764920

Subgroups — #14764920

Order 2816.

1092 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622653C211yesmaximal, characteristic
2#121×Dic11C211yesmaximal, characteristic
3C2×#10622587C211yesmaximal, characteristic, complemented
4#13069471C212yesmaximal, complemented
5#13069293C212yesmaximal, complemented
6#13069248C212yesmaximal, complemented
7#13068948C212yesmaximal, complemented
8#13068809C211yesmaximal, characteristic, complemented
9#13068552C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×D4×Dic11—21no—
16C2×D4×Dic11C2211yescharacteristic
17C22×#4324C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C2×C11×#102C2212yes—
20C2×C11×C22⋊C8C2211yescharacteristic
21#10622834C2211yescharacteristic
22#10622833—21no—
23#10622825C2211yescharacteristic
24C2×C11⋊#95—21no—
25C2×C11⋊#95—21no—
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×#66880C2212yes—
28C2×#66880C2212yes—
29C2×C8×Dic11C2212yes—
30#10622653C418yescomplemented
31#10622598C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622587—21no—
34#10622587—21no—
35#10622587C2212yes—
36#10622587C2212yes—
37C2×#66874C2212yes—
38C2×#66872C2212yes—
39#10622564—21no—
40C22⋊C4×Dic11—21no—
41C11×#340C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11—21no—
50C23×Dic11D411yescharacteristic
51C23×Dic11D411yescharacteristic
52C22×Dic22—21no—
53C22×Dic22—22no—
54C22×Dic22—42no—
55C22×Dic22—42no—
56C22×Dic22C2×C414yescomplemented
57C22×Dic22C2312yes—
58C22×C8×C11C2312yes—
59C11×#121—22no—
60C11×#121C2×C414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70D4×Dic11—42no—
71D4×Dic11—44no—
72C2×#4324—42no—
73C2×#4324—42no—
74C2×#4324C2×C418yescomplemented
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4×Dic11—21no—
79C2×C4×Dic11—42no—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C11×#102—42no—
86C11×C22⋊C8—22no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C22⋊(C11⋊C8)C2×C414yescomplemented
95#66880—42no—
96#66880—42no—
97C8×Dic11—42no—
98#66874C2×C418yescomplemented
99#66872—42no—
100#22041—111nomaximal, Sylow
101C24×C11—21no—
102C24×C11C2×D411yescharacteristic
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11C22×C412yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—24no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129C22×Dic11—41no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C22×Dic11SD1614yescomplemented
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C2×Dic22—24no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—48no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C2×Dic22—48no—
150C2×Dic22C22×C414yes—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4C22×C412yes—
159C11×C22⋊C4—24no—
160C22⋊Dic11—42no—
161C22⋊Dic11—42no—
162C22⋊Dic11—42no—
163C22⋊Dic11—42no—
164#4324—48no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—42no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8C22×C414yes—
176C2×#448—111no—
177C4×#121—111no—
178C2×#391—111no—
179#1968—112no—
180#1933—112no—
181#1927—112no—
182#1877—112no—
183#1874D1111yescharacteristic
184#1853—111no—
185#1787—111no—
186C4×C22⋊C8—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C4×D412yes—
199C23×C11C2×SD1612yes—
200C23×C11#13512yes—
201C23×C11C22×D411yescharacteristic
202D4×C11—24no—
203D4×C11—48no—
204D4×C11—42no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—84no—
216C2×C4×C11C4×D412yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11H(5,𝔽2)12yes—
220C2×C4×C11H(5,𝔽2)12yes—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—24no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C2×Dic11—48no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—84no—
243C2×Dic11C2×SD1612yes—
244C2×Dic11C2×SD1612yes—
245C2×Dic11#13712yes—
246Dic22—24no—
247Dic22—24no—
248Dic22—48no—
249Dic22—42no—
250Dic22—42no—
251C8×C11—42no—
252C11⋊C8—24no—
253C23×Q8—111no—
254C22×SD16—112no—
255C2×#121C2×D1111yescharacteristic
256C2×C4×D4—111no—
257C2×C4×D4—221no—
258C22×C4⋊C4C2×D1111yescharacteristic
259C22×C42—111no—
260#448—118no—
261C2×#106—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103—112no—
265C2×#102C2×D1112yes—
266C2×C22⋊C8—111no—
267C2×C22⋊C8C2×D1111yescharacteristic
268C2×C4×C8—112no—
269#391—112no—
270#391—112no—
271#391—221no—
272#391—221no—
273#390—111no—
274#389—111no—
275#388—221no—
276#386—221no—
277#380—111no—
278C4×C4⋊C4—111no—
279C4×C22⋊C4—221no—
280C2×#95—221no—
281C2×#95—221no—
282#340—112no—
283#340C2×D1112yes—
284#336—112no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11C4×SD1614yes—
299C22×C11C2×C4×D411yescharacteristic
300C22×C11#53411yescharacteristic
301C22×C11#53511yescharacteristic
302C22×C11C22×SD1611yescharacteristic
303C22×C11C2×#13511yescharacteristic
304C22×C11C2×#13711yescharacteristic
305C22×C11#57511yescharacteristic
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—82no—
309C4×C11#51812yes—
310C4×C11#53812yes—
311Dic11—22no—
312Dic11—22no—
313Dic11—22no—
314Dic11—44no—
315Dic11—41no—
316Dic11—81no—
317Dic11—81no—
318C22×Q8—114no—
319C22×Q8—112no—
320C22×Q8—221no—
321C22×Q8—222no—
322C22×Q8—442no—
323C22×Q8—442no—
324C22×D4—21no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—221no—
330C23×C4—221no—
331C23×C4C22×D1111yescharacteristic
332C2×SD16—118no—
333C2×SD16—442no—
334C2×SD16—442no—
335C22×C8—112no—
336C22×C8C22×D1112yes—
337#121—22no—
338#121C4×D1114yes—
339C4×D4—442no—
340C4×D4—444no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4C22×D1112yes—
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—221no—
358C2×C42—442no—
359#106—442no—
360#103—118no—
361#103—442no—
362#103—442no—
363#102—42no—
364C22⋊C8—22no—
365C22⋊C8—114no—
366C4×C8—442no—
367#95—222no—
368#95—222no—
369#95—222no—
370#95—222no—
371#95—221no—
372#95—221no—
373#95—221no—
374C2×C11—24no—
375C2×C11—82no—
376C2×C11#232111yescharacteristic
377C2×C11C2×C4×SD1611yescharacteristic
378C2×C11C4×#13711yescharacteristic
379C2×C11#318711yescharacteristic
380C2×C11#319011yescharacteristic
381C2×C11#320611yescharacteristic
382C2×C11#321111yescharacteristic
383C24—21no—
384C24D4×D1111yescharacteristic
385C2×Q8—114no—
386C2×Q8—224no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—222no—
392C2×Q8—448no—
393C2×Q8—442no—
394C2×Q8—442no—
395C2×Q8—448no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4C2×C4×D1112yes—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—114no—
414C22×C4—111no—
415C22×C4—222no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—442no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4—441no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4C2×C4×D1112yes—
430C22×C4D4×D1111yescharacteristic
431C22×C4#434112yes—
432C22×C4C23×D1111yescharacteristic
433SD16—448no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—114no—
438C2×C8—222no—
439C2×C8—222no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C4⋊C4—442no—
447C4⋊C4C2×C4×D1112yes—
448C22⋊C4—24no—
449C22⋊C4—442no—
450C22⋊C4—442no—
451C22⋊C4—442no—
452C22⋊C4—442no—
453C42—222no—
454C42—222no—
455C42—441no—
456C42—441no—
457C42—442no—
458C11#2204111yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—22no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23(C22⋊D11)⋊C412yes—
471C23#6696512yes—
472C23SD16×D1112yes—
473C23C2×D4×D1111yescharacteristic
474Q8—224no—
475Q8—224no—
476Q8—448no—
477Q8—442no—
478Q8—442no—
479D4—24no—
480D4—48no—
481D4—42no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—84no—
493C2×C4—112no—
494C2×C4—112no—
495C2×C4—112no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—224no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—444no—
507C2×C4—444no—
508C2×C4—448no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—884no—
518C2×C4(C22⋊D11)⋊C412yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4#6703712yes—
522C2×C4#6704212yes—
523C8—42no—
524C8—224no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22#1062237114yes—
539C22C2×(C22⋊D11)⋊C411yescharacteristic
540C22#1062312311yescharacteristic
541C22#1062318411yescharacteristic
542C22C2×#6696511yescharacteristic
543C22C2×SD16×D1111yescharacteristic
544C22#1062330411yescharacteristic
545C22D11×#13711yescharacteristic
546C4—22no—
547C4—42no—
548C4—82no—
549C4—222no—
550C4—222no—
551C4—222no—
552C4—441no—
553C4—444no—
554C4—881no—
555C4—881no—
556C4#1062307612yes—
557C4#1062314812yes—
558C2—24no—
559C2—82no—
560C2#1307127911yescharacteristic
561C2C2×#1062237111yescharacteristic
562C2#1307744011yescharacteristic
563C2#1307937511yescharacteristic
564C2#1307939611yescharacteristic
565C2#1307953911yescharacteristic
566C2#1307957811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenter#1874D11
hypocenterC11#22041
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
3. C2×#10622587C2semidirect
4. #13069471C2semidirect
5. #13069293C2semidirect
6. #13069248C2semidirect
7. #13068948C2semidirect
8. #13068809C2semidirect
9. #13068552C2semidirect
10. C22⋊C8×Dic11C2semidirect
30. #10622653C4semidirect
56. C22×Dic22C2×C4semidirect
74. C2×#4324C2×C4semidirect
94. C22⋊(C11⋊C8)C2×C4semidirect
98. #66874C2×C4semidirect
135. C22×Dic11SD16semidirect
458. C11#22041semidirect

Maximal subgroups

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

subgroupindex
C2×#106226532
#121×Dic112
C2×#106225872
#130694712
#130692932
#130692482
#130689482
#130688092
#130685522
C22⋊C8×Dic112
C11×#18742
#2204111