Finite Group Databasebeta

← #14773231

Subgroups — #14773231

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×#67003C211yesmaximal, characteristic
2#13077281C211yesmaximal, characteristic, complemented
3#13069319C212yesmaximal, complemented
4#13069212C212yesmaximal, complemented
5#13068943C212yesmaximal
6#13068753C211yesmaximal, characteristic, complemented
7#13068636C211yesmaximal, characteristic, complemented
8#13068633C211yesmaximal, characteristic, complemented
9#13068481C211yesmaximal, characteristic, complemented
10#13068451C212yesmaximal, complemented
11C11×#2906C211yesmaximal, characteristic, complemented
12C2×C11×#131C2212yes—
13C4×C11×#41C2211yescharacteristic
14C2×#67003C2211yescharacteristic
15C4×#4339C2211yescharacteristic
16C11×#424—22no—
17C11×#424C2212yes—
18C11×#423—21no—
19C11×#423C2211yescharacteristic
20C2×C11×C4⋊C8—21no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×#66901C2212yes—
23#10622846C2211yescharacteristic
24C2×#66889C2212yes—
25#10622723C2212yes—
26#10622714C2212yes—
27C2×C8×Dic11C2212yes—
28C4×#4326C411yescharacteristic, complemented
29C4×#4326C411yescharacteristic, complemented
30C4×#4325C411yescharacteristic, complemented
31C4×#4325C411yescharacteristic, complemented
32C4×#4324C411yescharacteristic, complemented
33C4×#4324C411yescharacteristic, complemented
34C4×#4323C411yescharacteristic, complemented
35C4×#4323C411yescharacteristic, complemented
36#10622615C2211yescharacteristic
37#10622611C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622453—22no—
42#10622448—21no—
43#10622446—21no—
44#10622196C2212yes—
45#10622196C2212yes—
46#10622193C2212yes—
47#10622188C2212yes—
48#10622170C2212yes—
49C2×C11×#41C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C11×#131—24no—
52C11×#131—42no—
53C2×C11×M16—22no—
54C2×C11×M16C2312yes—
55C22×C8×C11—22no—
56C22×C8×C11C2312yes—
57C4×Q8×C11C2×C411yescharacteristic
58C4×Q8×C11C2×C411yescharacteristic
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11C2×C411yescharacteristic
62C4×D4×C11C2×C411yescharacteristic
63C11×#117—21no—
64C11×#117C2311yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67#67003—22no—
68#67003—22no—
69C2×#4326C2×C411yescharacteristic
70C2×#4325C2×C411yescharacteristic
71C2×#4324C2×C411yescharacteristic
72C2×#4323C2×C411yescharacteristic
73C4×C22⋊D11—21no—
74C4×C22⋊D11—21no—
75#66979C2311yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4×Dic11C2312yes—
78C2×#4318C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C4×D44C2×C411yescharacteristic
82C4×D44C2×C411yescharacteristic
83#66925—21no—
84C42×D11—21no—
85C4×Dic22C2×C411yescharacteristic
86C4×Dic22C2×C411yescharacteristic
87C11×C4⋊C8—22no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8D411yescharacteristic
92C11×C4⋊C8D411yescharacteristic
93C11×C4⋊C8D412yes—
94#66901—24no—
95#66899C2×C411yescharacteristic
96#66899C2×C411yescharacteristic
97#66896C2×C411yescharacteristic
98#66896C2×C411yescharacteristic
99C11⋊#95—21no—
100#66889—42no—
101(C2×D11)⋊C8—22no—
102(C2×D11)⋊C8—22no—
103#66879—22no—
104C8×Dic11—22no—
105C8×Dic11—42no—
106#66874C2×C411yescharacteristic
107#66874C2×C411yescharacteristic
108#66873C2×C411yescharacteristic
109#66873C2×C411yescharacteristic
110#66872C2×C411yescharacteristic
111#66872C2×C411yescharacteristic
112#66871C2×C411yescharacteristic
113#66871C2×C411yescharacteristic
114C4⋊(C11⋊C8)—21no—
115C4⋊(C11⋊C8)—21no—
116C4×C11⋊C8C2×C411yescharacteristic
117C4×C11⋊C8C2×C411yescharacteristic
118C4×C11⋊C8C2×C411yescharacteristic
119C4×C11⋊C8C2×C411yescharacteristic
120#22783—111nomaximal, Sylow
121C11×#41—21no—
122C11×#41—21no—
123C11×#41#4112yes—
124C11×#41#4112yes—
125C2×Q8×C11C22×C411yescharacteristic
126C2×D4×C11—21no—
127C2×D4×C11C22×C411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11#4111yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—21no—
135C22×Dic11—22no—
136#4339—21no—
137#4339—21no—
138#4339—21no—
139#4339—21no—
140C2×D44C22×C411yescharacteristic
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×Dic22C22×C411yescharacteristic
145C11×M16—22no—
146C11×M16—22no—
147C11×M16—44no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—44no—
152C2×C8×C11C2×D412yes—
153C2×C8×C11C2×D412yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4C22×C411yescharacteristic
157C11×C4⋊C4C22×C411yescharacteristic
158C11×C22⋊C4—21no—
159C11×C22⋊C4—21no—
160C11×C22⋊C4—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11C22×C411yescharacteristic
165C42×C11C22×C411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C22⋊Dic11—21no—
169#4326—22no—
170#4325—22no—
171#4324—22no—
172#4323—22no—
173(C2×D11)⋊C4—21no—
174(C2×D11)⋊C4—21no—
175C4⋊Dic11—24no—
176C4⋊Dic11C22×C411yescharacteristic
177C4⋊Dic11C22×C411yescharacteristic
178Dic11⋊C4—21no—
179Dic11⋊C4—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185#4318—22no—
186#4318—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8C22×C411yescharacteristic
193C2×C11⋊C8C22×C411yescharacteristic
194C2×C11⋊C8C22×C411yescharacteristic
195C2×C11⋊C8C22×C411yescharacteristic
196C4×#135—111no—
197#2925—111no—
198#2906D1111yescharacteristic, complemented
199#1937—112no—
200#1922—112no—
201#1876—112no—
202#1837—111no—
203#1806—111no—
204#1806—111no—
205C8×C4⋊C4—111no—
206#1764—112no—
207C23×C11—21no—
208C23×C11C2×#4111yescharacteristic
209C22×D11—21no—
210Q8×C11—21no—
211Q8×C11#11712yes—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—21no—
215D4×C11#11712yes—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—81no—
225C2×C4×C11C4×D411yescharacteristic
226C2×C4×C11C4×D411yescharacteristic
227C2×C4×C11C4×D411yescharacteristic
228C2×C4×C11C4×D411yescharacteristic
229C2×C4×C11C23×C411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C22⋊D11—41no—
236C22⋊D11—41no—
237C2×Dic11—24no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243D44—21no—
244D44—21no—
245C4×D11—41no—
246C4×D11—41no—
247C4×D11—42no—
248C4×D11—81no—
249Dic22—21no—
250Dic22—21no—
251C8×C11—22no—
252C8×C11—22no—
253C8×C11—42no—
254C11⋊C8—21no—
255C11⋊C8—21no—
256C11⋊C8—21no—
257C11⋊C8—21no—
258C11⋊C8—42no—
259C2×#135—111no—
260C2×#131C2×D1112yes—
261C4×#41—111no—
262C4×#41C2×D1111yescharacteristic
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—22no—
276#424C2×D1112yes—
277#423—21no—
278#423—111no—
279#423C2×D1111yescharacteristic
280C2×C4⋊C8—21no—
281C2×C4⋊C8C2×D1111yescharacteristic
282C2×#104—112no—
283C2×#104—112no—
284#416—111no—
285#416—111no—
286#408—112no—
287#405—112no—
288C2×C4×C8—111no—
289C2×C4×C8—112no—
290C4×C4⋊C4—111no—
291#341—112no—
292#341—112no—
293#339—112no—
294#339—112no—
295#336—112no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—22no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11C2×C4×D411yescharacteristic
302C22×C11#55211yescharacteristic
303C22×C11#55311yescharacteristic
304C2×D11—41no—
305C2×D11—41no—
306C2×D11—41no—
307C4×C11—22no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—41no—
312C4×C11—41no—
313C4×C11#44312yes—
314C4×C11C2×#11711yescharacteristic
315C4×C11#52011yescharacteristic
316C4×C11#54611yescharacteristic
317C4×C11#54811yescharacteristic
318Dic11—44no—
319Dic11—41no—
320Dic11—41no—
321Dic11—41no—
322C2×#41—111no—
323C2×#41C22×D1111yescharacteristic
324#135—222no—
325#135—222no—
326C2×Q16—111no—
327C2×SD16—111no—
328C2×SD16—111no—
329C2×D8—111no—
330#131—24no—
331#131—42no—
332C2×M16—22no—
333C2×M16—112no—
334C2×M16C22×D1112yes—
335C22×C8—22no—
336C22×C8—111no—
337C22×C8—111no—
338C22×C8C22×D1112yes—
339C4×Q8—111no—
340C4×Q8—111no—
341C4×Q8C4×D1111yescharacteristic
342C4×Q8C4×D1111yescharacteristic
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—111no—
346C4×D4—111no—
347C4×D4—221no—
348C4×D4—221no—
349C4×D4C4×D1111yescharacteristic
350C4×D4C4×D1111yescharacteristic
351#117—21no—
352#117—111no—
353#117—221no—
354#117C22×D1111yescharacteristic
355C2×C4⋊C4—221no—
356C2×C42—21no—
357C2×C42—112no—
358C2×C42—221no—
359C2×C42C22×D1111yescharacteristic
360#107—111no—
361#107—111no—
362#106—111no—
363#106—111no—
364C4⋊C8—22no—
365C4⋊C8—22no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—221no—
369C4⋊C8—221no—
370C4⋊C8C22⋊D1111yescharacteristic
371C4⋊C8C22⋊D1111yescharacteristic
372C4⋊C8C22⋊D1112yes—
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—111no—
387C4×C8—111no—
388C4×C8—111no—
389C4×C8—111no—
390C4×C8—222no—
391C4×C8—442no—
392#95—221no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—42no—
396C2×C11#235211yescharacteristic
397C2×C11C2×#44311yescharacteristic
398C2×C11#295711yescharacteristic
399D11—81no—
400#41—21no—
401#41—21no—
402#41—221no—
403#41—221no—
404#41—221no—
405#41—221no—
406#41#434112yes—
407#41#434312yes—
408C2×Q8—111no—
409C2×Q8C2×C4×D1111yescharacteristic
410C2×D4—21no—
411C2×D4—111no—
412C2×D4—221no—
413C2×D4C2×C4×D1111yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4#433911yescharacteristic
422C22×C4#433911yescharacteristic
423C22×C4C23×D1111yescharacteristic
424Q16—222no—
425SD16—222no—
426SD16—222no—
427D8—222no—
428M16—22no—
429M16—22no—
430M16—44no—
431M16—222no—
432M16—222no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—44no—
437C2×C8—111no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—111no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—222no—
446C2×C8C2×C22⋊D1112yes—
447C2×C8C2×C22⋊D1112yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—111no—
451C4⋊C4—111no—
452C4⋊C4—224no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4C2×C4×D1111yescharacteristic
456C4⋊C4C2×C4×D1111yescharacteristic
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—221no—
461C22⋊C4—221no—
462C22⋊C4—221no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—221no—
467C42—221no—
468C42—221no—
469C42—222no—
470C42—222no—
471C42C2×C4×D1111yescharacteristic
472C42C2×C4×D1111yescharacteristic
473C42C2×C22⋊D1111yescharacteristic
474C42C2×C22⋊D1111yescharacteristic
475C11#2278311yescharacteristic, complemented, Sylow
476C23—21no—
477C23—221no—
478C23C2×#433911yescharacteristic
479Q8—21no—
480Q8—221no—
481Q8—221no—
482Q8#6694512yes—
483D4—22no—
484D4—22no—
485D4—21no—
486D4—221no—
487D4—221no—
488D4—441no—
489D4—441no—
490D4#6694512yes—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—81no—
500C2×C4—224no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—881no—
510C2×C4C4×C22⋊D1111yescharacteristic
511C2×C4C4×C22⋊D1111yescharacteristic
512C2×C4C4×C22⋊D1111yescharacteristic
513C2×C4C4×C22⋊D1111yescharacteristic
514C2×C4C22×C4×D1111yescharacteristic
515C2×C4C2×#434111yescharacteristic
516C2×C4#6703711yescharacteristic
517C2×C4C2×#434311yescharacteristic
518C2×C4#6704011yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—22no—
521C8—22no—
522C8—42no—
523C8—221no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—442no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—441no—
534C22—441no—
535C22—441no—
536C22#1062304411yescharacteristic
537C22#1062304511yescharacteristic
538C22C2×C4×C22⋊D1111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—22no—
543C4—41no—
544C4—41no—
545C4—444no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4#1062275712yes—
550C4C2×#6694511yescharacteristic
551C4#1062303511yescharacteristic
552C4#1062333711yescharacteristic
553C4#1062334811yescharacteristic
554C2—21no—
555C2—21no—
556C2—42no—
557C2—881no—
558C2#1307154111yescharacteristic
559C2C2×#1062275711yescharacteristic
560C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2906C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenter#2906D11
hypocenterC11#22783
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #13077281C2semidirect
3. #13069319C2semidirect
4. #13069212C2semidirect
6. #13068753C2semidirect
7. #13068636C2semidirect
8. #13068633C2semidirect
9. #13068481C2semidirect
10. #13068451C2semidirect
11. C11×#2906C2semidirect
28. C4×#4326C4semidirect
29. C4×#4326C4semidirect
30. C4×#4325C4semidirect
31. C4×#4325C4semidirect
32. C4×#4324C4semidirect
33. C4×#4324C4semidirect
34. C4×#4323C4semidirect
35. C4×#4323C4semidirect
198. #2906D11semidirect
475. C11#22783semidirect

Maximal subgroups

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

subgroupindex
C4×#670032
#130772812
#130693192
#130692122
#130689432
#130687532
#130686362
#130686332
#130684812
#130684512
C11×#29062
#2278311