Finite Group Databasebeta

← #14773232

Subgroups — #14773232

Order 2816.

752 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66957C211yesmaximal, characteristic
2#13077284C211yesmaximal, characteristic, complemented
3#13077185C211yesmaximal, characteristic, complemented
4#13069318C212yesmaximal, complemented
5#13069214C212yesmaximal, complemented
6#13068944C212yesmaximal
7#13068633C211yesmaximal, characteristic, complemented
8#13068633C211yesmaximal, characteristic, complemented
9C8×C4⋊Dic11C211yesmaximal, characteristic, complemented
10#13068452C212yesmaximal, complemented
11C11×#1837C211yesmaximal, characteristic, complemented
12C2×#66960C2212yes—
13C2×#66957C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C4×#4339C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C11×#423C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66889C2212yes—
20C2×#66889C2212yes—
21#10622742C2212yes—
22#10622735C2212yes—
23#10622732C2212yes—
24#10622726C2211yescharacteristic
25#10622726C2211yescharacteristic
26#10622719C2211yescharacteristic
27C2×C8×Dic11C2212yes—
28C4×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622453—22no—
31#10622452—22no—
32#10622450—21no—
33#10622448—21no—
34#10622446—21no—
35D11×C4⋊C8—21no—
36C4×Dic44C411yescharacteristic, complemented
37C4×Dic44C411yescharacteristic, complemented
38C4×D88C411yescharacteristic, complemented
39C4×D88C411yescharacteristic, complemented
40C4×#4314C411yescharacteristic, complemented
41C4×#4314C411yescharacteristic, complemented
42C4×#4314C411yescharacteristic, complemented
43C4×#4314C411yescharacteristic, complemented
44C11×#341C2212yes—
45C11×#341C2212yes—
46#10622193C2212yes—
47#10622193C2212yes—
48#10622188C2212yes—
49C2×#4339C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C2×C11×M16C2312yes—
52C2×C11×M16C2312yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C4×C22⋊D11—21no—
57C4×C22⋊D11—21no—
58C4×C22⋊D11—21no—
59C4×C22⋊D11—21no—
60#66979C2311yescharacteristic
61#66979C2311yescharacteristic
62C2×C4⋊Dic11—21no—
63C2×C4×Dic11C2312yes—
64C22×C11⋊C8C2312yes—
65#66960—24no—
66#66960—42no—
67C2×Dic44C2×C411yescharacteristic
68#66957—22no—
69#66957—22no—
70C2×D88C2×C411yescharacteristic
71C2×#4314C2×C411yescharacteristic
72C2×#4314C2×C411yescharacteristic
73C2×#4313—22no—
74C2×C8×D11—22no—
75C4×D44C2×C411yescharacteristic
76C4×D44C2×C411yescharacteristic
77C4×D44C2×C411yescharacteristic
78C4×D44C2×C411yescharacteristic
79#66925—21no—
80#66925—21no—
81C42×D11—21no—
82C42×D11—21no—
83C4×Dic22C2×C411yescharacteristic
84C4×Dic22C2×C411yescharacteristic
85C4×Dic22C2×C411yescharacteristic
86C4×Dic22C2×C411yescharacteristic
87C11×C4⋊C8—21no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C4×C8×C11C2×C411yescharacteristic
92C4×C8×C11C2×C411yescharacteristic
93C4×C8×C11C2×C411yescharacteristic
94C4×C8×C11C2×C411yescharacteristic
95C11⋊#95—21no—
96#66889—24no—
97#66889—42no—
98#66885C2×C411yescharacteristic
99#66885C2×C411yescharacteristic
100#66885C2×C411yescharacteristic
101#66885C2×C411yescharacteristic
102(C2×D11)⋊C8—22no—
103(C2×D11)⋊C8—22no—
104#66882C2×C411yescharacteristic
105#66882C2×C411yescharacteristic
106#66881C2×C411yescharacteristic
107#66881C2×C411yescharacteristic
108#66880C2×C411yescharacteristic
109#66880C2×C411yescharacteristic
110#66880C2×C411yescharacteristic
111#66880C2×C411yescharacteristic
112#66879—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—22no—
116C8×Dic11—42no—
117C4⋊(C11⋊C8)D411yescharacteristic
118C4⋊(C11⋊C8)D411yescharacteristic
119C4⋊(C11⋊C8)D412yes—
120#22783—111nomaximal, Sylow
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—21no—
125C2×C22⋊D11—21no—
126C22×Dic11—22no—
127#4339—21no—
128#4339—21no—
129#4339—21no—
130#4339—21no—
131#4339—21no—
132#4339—21no—
133#4339#4112yes—
134#4339#4112yes—
135C2×D44C22×C411yescharacteristic
136C2×D44C22×C411yescharacteristic
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×Dic22C22×C411yescharacteristic
144C2×Dic22C22×C411yescharacteristic
145C11×M16—22no—
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C22×C411yescharacteristic
156C2×C8×C11C22×C411yescharacteristic
157C2×C8×C11C22×C411yescharacteristic
158C2×C8×C11C22×C411yescharacteristic
159C42×C11C22×C411yescharacteristic
160C42×C11C22×C411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C22⋊Dic11—21no—
164C22⋊Dic11—21no—
165(C2×D11)⋊C4—21no—
166(C2×D11)⋊C4—21no—
167(C2×D11)⋊C4—21no—
168(C2×D11)⋊C4—21no—
169C4⋊Dic11—24no—
170C4⋊Dic11C22×C411yescharacteristic
171C4⋊Dic11C22×C411yescharacteristic
172C4⋊Dic11C22×C411yescharacteristic
173C4⋊Dic11C22×C411yescharacteristic
174Dic11⋊C4—21no—
175Dic11⋊C4—21no—
176Dic11⋊C4—21no—
177Dic11⋊C4—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2×D412yes—
189C2×C11⋊C8C2×D412yes—
190Dic44—22no—
191D88—22no—
192#4314—22no—
193#4314—22no—
194#4313—44no—
195C8×D11—44no—
196C4×#135—111no—
197#2925—111no—
198#2906—111no—
199#1937—112no—
200#1922—112no—
201#1876—112no—
202#1837D1111yescharacteristic, complemented
203#1806—111no—
204#1806—111no—
205C8×C4⋊C4—111no—
206#1764—112no—
207C23×C11C2×#4111yescharacteristic
208C22×D11—21no—
209C22×D11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11C4×D411yescharacteristic
213C2×C4×C11C4×D411yescharacteristic
214C2×C4×C11C4×D411yescharacteristic
215C2×C4×C11C4×D411yescharacteristic
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222C22⋊D11—22no—
223C22⋊D11—22no—
224C22⋊D11—41no—
225C22⋊D11—41no—
226C2×Dic11—21no—
227C2×Dic11—24no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235D44—21no—
236D44—21no—
237D44—21no—
238D44#11712yes—
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—41no—
242C4×D11—41no—
243C4×D11—42no—
244C4×D11—42no—
245C4×D11—81no—
246C4×D11—81no—
247Dic22—21no—
248Dic22—21no—
249Dic22—21no—
250Dic22#11712yes—
251C8×C11—21no—
252C8×C11—21no—
253C8×C11—21no—
254C8×C11—21no—
255C8×C11—42no—
256C8×C11—42no—
257C11⋊C8—22no—
258C11⋊C8—22no—
259C2×#135—111no—
260C2×#131—112no—
261C4×#41—111no—
262C4×#41—111no—
263C4×Q16—111no—
264C4×Q16—111no—
265C4×SD16—111no—
266C4×SD16—111no—
267C4×SD16—111no—
268C4×SD16—111no—
269C4×D8—111no—
270C4×D8—111no—
271#433—222no—
272#432—221no—
273#431—221no—
274#427—111no—
275#424—112no—
276#424—222no—
277#423—221no—
278#423C2×D1111yescharacteristic
279#423C2×D1111yescharacteristic
280C2×C4⋊C8—111no—
281C2×C4⋊C8—221no—
282C2×#104—112no—
283C2×#104—112no—
284#416—111no—
285#416—111no—
286#408—112no—
287#405—112no—
288C2×C4×C8—112no—
289C2×C4×C8C2×D1111yescharacteristic
290C4×C4⋊C4—111no—
291#341C2×D1112yes—
292#341C2×D1112yes—
293#339—112no—
294#339—112no—
295#336—112no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11C2×C4×D411yescharacteristic
299C22×C11#55211yescharacteristic
300C22×C11#55311yescharacteristic
301C2×D11—22no—
302C2×D11—41no—
303C2×D11—41no—
304C2×D11—41no—
305C2×D11—41no—
306C2×D11—41no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11#44312yes—
311C4×C11C2×#11711yescharacteristic
312C4×C11#52011yescharacteristic
313C4×C11#54611yescharacteristic
314C4×C11#54811yescharacteristic
315Dic11—22no—
316Dic11—44no—
317Dic11—41no—
318Dic11—41no—
319Dic11—41no—
320Dic11—41no—
321Dic11—41no—
322C2×#41—111no—
323C2×#41—111no—
324#135—222no—
325#135—222no—
326C2×Q16—111no—
327C2×SD16—111no—
328C2×SD16—111no—
329C2×D8—111no—
330#131—224no—
331#131—442no—
332C2×M16—222no—
333C2×M16C22×D1112yes—
334C2×M16C22×D1112yes—
335C22×C8—112no—
336C22×C8—222no—
337C22×C8C22×D1111yescharacteristic
338C22×C8C22×D1111yescharacteristic
339C4×Q8—111no—
340C4×Q8—111no—
341C4×Q8—111no—
342C4×Q8—111no—
343C4×D4—111no—
344C4×D4—111no—
345C4×D4—111no—
346C4×D4—111no—
347C4×D4—221no—
348C4×D4—221no—
349C4×D4—221no—
350C4×D4—221no—
351#117—111no—
352#117—111no—
353#117—221no—
354#117—221no—
355C2×C4⋊C4—221no—
356C2×C42—112no—
357C2×C42—221no—
358C2×C42—221no—
359C2×C42C22×D1111yescharacteristic
360#107—111no—
361#107—111no—
362#106—111no—
363#106—111no—
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—111no—
369C4⋊C8—111no—
370C4⋊C8—112no—
371C4⋊C8—222no—
372C4⋊C8—222no—
373#104—224no—
374#104—442no—
375#103—111no—
376#103—111no—
377#103—111no—
378#103—111no—
379#102—111no—
380#102—111no—
381#102—111no—
382#102—111no—
383C22⋊C8—222no—
384C22⋊C8—222no—
385#97—222no—
386C4×C8—222no—
387C4×C8—442no—
388C4×C8C4×D1111yescharacteristic
389C4×C8C4×D1111yescharacteristic
390C4×C8C4×D1111yescharacteristic
391C4×C8C4×D1111yescharacteristic
392#95—221no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11#235211yescharacteristic
396C2×C11C2×#44311yescharacteristic
397C2×C11#295711yescharacteristic
398D11—42no—
399D11—81no—
400#41—112no—
401#41—112no—
402#41—221no—
403#41—221no—
404#41—221no—
405#41—221no—
406#41—221no—
407#41—221no—
408C2×Q8—111no—
409C2×Q8—111no—
410C2×D4—111no—
411C2×D4—111no—
412C2×D4—221no—
413C2×D4—221no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4#434311yescharacteristic
422C22×C4#434311yescharacteristic
423C22×C4C23×D1111yescharacteristic
424Q16—222no—
425SD16—222no—
426SD16—222no—
427D8—222no—
428M16—22no—
429M16—22no—
430M16—22no—
431M16—22no—
432M16—444no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—112no—
440C2×C8—112no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—444no—
444C2×C8C2×C4×D1111yescharacteristic
445C2×C8C2×C4×D1111yescharacteristic
446C2×C8C2×C4×D1111yescharacteristic
447C2×C8C2×C4×D1111yescharacteristic
448C4⋊C4—111no—
449C4⋊C4—111no—
450C4⋊C4—111no—
451C4⋊C4—111no—
452C4⋊C4—224no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C22⋊C4—221no—
458C22⋊C4—221no—
459C22⋊C4—221no—
460C22⋊C4—221no—
461C22⋊C4—221no—
462C22⋊C4—221no—
463C42—221no—
464C42—221no—
465C42—221no—
466C42—221no—
467C42—221no—
468C42—221no—
469C42—222no—
470C42—222no—
471C42C2×C4×D1111yescharacteristic
472C42C2×C4×D1111yescharacteristic
473C42D4×D1111yescharacteristic
474C42D4×D1111yescharacteristic
475C11#2278311yescharacteristic, complemented, Sylow
476C23—221no—
477C23—221no—
478C23C2×#434311yescharacteristic
479Q8—112no—
480Q8—221no—
481Q8—221no—
482Q8—221no—
483D4—112no—
484D4—222no—
485D4—222no—
486D4—221no—
487D4—221no—
488D4—221no—
489D4—441no—
490D4—441no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—221no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—881no—
509C2×C4—881no—
510C2×C4#6694611yescharacteristic
511C2×C4#6694611yescharacteristic
512C2×C4#6694611yescharacteristic
513C2×C4#6694611yescharacteristic
514C2×C4C22×C4×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4#41×D1111yescharacteristic
517C2×C4#41×D1111yescharacteristic
518C2×C4#6704211yescharacteristic
519C2×C4#6704311yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—42no—
525C8—42no—
526C8—222no—
527C8—222no—
528C22—21no—
529C22—21no—
530C22—222no—
531C22—441no—
532C22—441no—
533C22—441no—
534C22—441no—
535C22—441no—
536C22C2×#6694611yescharacteristic
537C22#1062322511yescharacteristic
538C22#1062322611yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—222no—
543C4—444no—
544C4—441no—
545C4—441no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4#1062250812yes—
550C4D11×#11711yescharacteristic
551C4#1062305411yescharacteristic
552C4#1062320711yescharacteristic
553C4#1062320811yescharacteristic
554C2—21no—
555C2—21no—
556C2—442no—
557C2—881no—
558C2#1307154211yescharacteristic
559C2C2×#1062250811yescharacteristic
560C2#1307753211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1837C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C22
cosocleC22×C4×C11C24
hypercenter#1837D11
hypocenterC11#22783
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1837

Complements

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

NH ≅ G/Ntype
2. #13077284C2semidirect
3. #13077185C2semidirect
4. #13069318C2semidirect
5. #13069214C2semidirect
7. #13068633C2semidirect
8. #13068633C2semidirect
9. C8×C4⋊Dic11C2semidirect
10. #13068452C2semidirect
11. C11×#1837C2semidirect
36. C4×Dic44C4semidirect
37. C4×Dic44C4semidirect
38. C4×D88C4semidirect
39. C4×D88C4semidirect
40. C4×#4314C4semidirect
41. C4×#4314C4semidirect
42. C4×#4314C4semidirect
43. C4×#4314C4semidirect
202. #1837D11semidirect
475. C11#22783semidirect

Maximal subgroups

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

subgroupindex
C4×#669572
#130772842
#130771852
#130693182
#130692142
#130689442
#130686332
C8×C4⋊Dic112
#130684522
C11×#18372
#2278311