Finite Group Databasebeta

← #15625218

Subgroups — #15625218

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic
2#13079643C218yesmaximal, complemented
3#13079564C214yesmaximal, complemented
4#13079541C214yesmaximal, complemented
5#13079073C212yesmaximal, complemented
6#13078996C212yesmaximal, complemented
7#13078099C214yesmaximal, complemented
8#13077850C214yesmaximal, complemented
9#13077249C211yesmaximal, characteristic, complemented
10C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
11C23×Q8×C11C2212yes—
12C2×C11×C4⋊Q8—22no—
13C2×C11×C4⋊Q8—22no—
14C2×C11×C4⋊Q8—22no—
15C2×C11×C4⋊Q8C2214yes—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×C4⋊Q8C2214yes—
19C22×C11×C4⋊C4—22no—
20C22×C42×C11C2211yescharacteristic
21C2×#66995C2218yes—
22#10623322—22no—
23#10623322C2212yes—
24#10623010—22no—
25#10623010—22no—
26#10623010C2214yes—
27#10623008C2211yescharacteristic
28#10623008C2212yes—
29C4×#4339—22no—
30C4×#4339C2212yes—
31#10623001C2211yescharacteristic
32#10623001C2212yes—
33#10622841C22116yes—
34#10622840C22116yes—
35#10622838C2218yes—
36#10622820C2212yes—
37#10622705C2214yescomplemented
38#10622703C22116yescomplemented
39#10622699C2218yescomplemented
40#10622698C2214yescomplemented
41#10622696C22116yescomplemented
42#10622695C2218yescomplemented
43#10622694C2218yescomplemented
44#10622539C2214yes—
45#10622538C2214yes—
46#10622537C2212yes—
47C4×#4318C2212yes—
48C22×Q8×C11—24no—
49C22×Q8×C11—22no—
50C22×Q8×C11—48no—
51C22×Q8×C11C2314yes—
52C22×Q8×C11C2318yes—
53C23×C4×C11—22no—
54C23×C4×C11D412yes—
55C23×C4×C11C2311yescharacteristic
56C2×#4339—22no—
57C2×#4339C2312yes—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—24no—
64C11×C4⋊Q8—24no—
65C11×C4⋊Q8C2314yes—
66C11×C4⋊Q8C2314yes—
67C11×C4⋊Q8C2318yes—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C42×C11D412yes—
75C2×C42×C11D412yes—
76C2×C42×C11D412yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2312yes—
81#67006—22no—
82C2×#4326C23116yes—
83#66995—416no—
84C2×#4325C23116yes—
85#66983—22no—
86#66983—22no—
87#66983C2314yes—
88#66982—22no—
89#66982—24no—
90C4×C22⋊D11—24no—
91C4×C22⋊D11—24no—
92C4×C22⋊D11—24no—
93#66979—22no—
94#66979C2312yes—
95#66977—22no—
96#66977—22no—
97#66977C2314yes—
98C2×#4318C2314yes—
99#66929—24no—
100#66928—22no—
101#66928C2312yes—
102#66927C2311yescharacteristic
103C4×D44—22no—
104C4×D44—22no—
105C4×D44C2314yes—
106#66925—24no—
107#66925—22no—
108C42×D11—22no—
109#66923—22no—
110#66923C2312yes—
111#66922C2311yescharacteristic
112#66922C2312yes—
113C4×Dic22—22no—
114C4×Dic22—22no—
115C4×Dic22C2314yes—
116#66899C23132yes—
117C22⋊(C11⋊C8)C2318yes—
118C4⋊(C11⋊C8)C2318yes—
119#66867C2314yes—
120C4×C11⋊C8C2314yes—
121#60800—111nomaximal, Sylow
122C24×C11C2×D411yescharacteristic
123C2×Q8×C11—28no—
124C2×Q8×C11—24no—
125C2×Q8×C11—216no—
126C2×Q8×C11—416no—
127C2×Q8×C11—48no—
128C2×Q8×C11—416no—
129C2×Q8×C11C2418yes—
130C22×C4×C11—28no—
131C22×C4×C11—24no—
132C22×C4×C11—28no—
133C22×C4×C11—24no—
134C22×C4×C11—48no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—22no—
146C2×C22⋊D11—24no—
147#4339—28no—
148#4339—48no—
149C2×D44—22no—
150C2×D44C2412yes—
151C2×C4×D11—22no—
152C2×C4×D11—24no—
153C2×Dic22—22no—
154C2×Dic22C2412yes—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—28no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D412yes—
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D412yes—
166C42×C11C2411yescharacteristic
167C42×C11C2411yescharacteristic
168C42×C11C2412yes—
169C22⋊Dic11—22no—
170C22⋊Dic11—24no—
171#4326—416no—
172#4325—416no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—24no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11C2414yes—
179Dic11⋊C4—24no—
180Dic11⋊C4—24no—
181Dic11⋊C4—24no—
182C4×Dic11—22no—
183C4×Dic11—24no—
184#4318—28no—
185C2×C11⋊C8C2418yes—
186#3444—111no—
187C22×C4⋊Q8D1111yescharacteristic, complemented
188#3218—118no—
189#3209—114no—
190#3206—114no—
191#3152—112no—
192#3139—112no—
193#3039—114no—
194#3004—114no—
195#2920—111no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11C22×D411yescharacteristic
199C23×C11C22×D412yes—
200C22×D11—22no—
201Q8×C11—216no—
202Q8×C11—416no—
203Q8×C11—48no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—28no—
213C2×C4×C11—416no—
214C2×C4×C11—48no—
215C2×C4×C11#13718yescomplemented
216C2×C4×C11C22×D412yes—
217C2×C4×C11C22×D412yes—
218C2×C4×C11C22×D412yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D412yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11H(5,𝔽2)14yes—
223C2×C4×C11C2511yescharacteristic
224C22⋊D11—44no—
225C22⋊D11—48no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228D44—24no—
229D44—44no—
230C4×D11—44no—
231C4×D11—48no—
232Dic22—24no—
233Dic22—44no—
234C11⋊C8—28no—
235C23×Q8C2×D1112yes—
236C2×#137—118no—
237#533—111no—
238#533—112no—
239#532—112no—
240#532—111no—
241C2×C4⋊Q8—22no—
242C2×C4⋊Q8—22no—
243C2×C4⋊Q8—22no—
244C2×C4⋊Q8C2×D1112yes—
245C2×C4⋊Q8C2×D1114yes—
246C2×C4⋊Q8C2×D1114yes—
247C2×C4⋊Q8C2×D1112yes—
248#529—114no—
249#529—222no—
250#529—222no—
251#525—112no—
252#525—222no—
253C4×#41—112no—
254C4×#41—222no—
255C22×C4⋊C4—22no—
256C22×C42C2×D1111yescharacteristic
257#497—118no—
258#494—114no—
259#492—114no—
260#491—118no—
261#487—118no—
262#462—1116no—
263#461—1116no—
264#451—1116no—
265#448—1116no—
266#432—114no—
267#431—114no—
268#423—112no—
269#419—118no—
270#407—112no—
271C4×M16—112no—
272C22×C11—28no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11#53512yes—
277C22×C11C2×#13714yes—
278C22×C11C23×D411yescharacteristic
279C2×D11—42no—
280C2×D11—44no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—48no—
285C4×C11#53512yes—
286C4×C11C2×#13714yes—
287C4×C11C2×#13714yes—
288C4×C11C2×H(5,𝔽2)12yes—
289Dic11—42no—
290Dic11—44no—
291C2×#41—112no—
292C2×#41—222no—
293C22×Q8—24no—
294C22×Q8—22no—
295C22×Q8—48no—
296C22×Q8C22×D1114yes—
297C22×Q8C22×D1118yes—
298C23×C4—22no—
299C23×C4C22⋊D1112yes—
300C23×C4C22×D1111yescharacteristic
301#137—4416no—
302C2×Q16—1116no—
303C2×SD16—1116no—
304C2×M16—114no—
305C4⋊Q8—22no—
306C4⋊Q8—24no—
307C4⋊Q8—22no—
308C4⋊Q8—24no—
309C4⋊Q8—24no—
310C4⋊Q8—24no—
311C4⋊Q8—24no—
312C4⋊Q8—112no—
313C4⋊Q8—111no—
314C4⋊Q8C22×D1118yes—
315C4⋊Q8C22×D1114yes—
316C4⋊Q8C22×D1114yes—
317#127—111no—
318#126—224no—
319#125—112no—
320#125—222no—
321#124—112no—
322#124—222no—
323#123—222no—
324#123—224no—
325C22⋊Q8—114no—
326C22⋊Q8—222no—
327C22⋊Q8—222no—
328#121—114no—
329#121—222no—
330#121—222no—
331#120—222no—
332C4×Q8—114no—
333C4×Q8—222no—
334C4×Q8—222no—
335C4×D4—114no—
336C4×D4—224no—
337C4×D4—224no—
338C4×D4—224no—
339C4×D4—222no—
340C4×D4—222no—
341#117—112no—
342#117—222no—
343#117—222no—
344#117—224no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C42—222no—
352C2×C42C22⋊D1112yes—
353C2×C42C22⋊D1112yes—
354C2×C42C22⋊D1112yes—
355C2×C42C22×D1111yescharacteristic
356C2×C42C22×D1112yes—
357C2×C42C22×D1111yescharacteristic
358C2×C42C22×D1112yes—
359C4⋊C8—118no—
360#103—1132no—
361C22⋊C8—118no—
362#97—114no—
363C4×C8—114no—
364C2×C11—22no—
365C2×C11—24no—
366C2×C11C2×#53511yescharacteristic
367C2×C11C22×#13712yes—
368D11—82no—
369C24C2×C22⋊D1111yescharacteristic
370#41—228no—
371#41—448no—
372C2×Q8—28no—
373C2×Q8—24no—
374C2×Q8—216no—
375C2×Q8—416no—
376C2×Q8—48no—
377C2×Q8—416no—
378C2×Q8—112no—
379C2×Q8—222no—
380C2×Q8C23×D1118yes—
381C2×D4—112no—
382C2×D4—224no—
383C2×D4—222no—
384C2×D4—222no—
385C22×C4—28no—
386C22×C4—24no—
387C22×C4—28no—
388C22×C4—24no—
389C22×C4—48no—
390C22×C4—224no—
391C22×C4—222no—
392C22×C4C2×C22⋊D1112yes—
393C22×C4C2×C22⋊D1112yes—
394C22×C4C2×C22⋊D1112yes—
395C22×C4C2×C22⋊D1112yes—
396C22×C4C2×C22⋊D1112yes—
397C22×C4C2×C22⋊D1112yes—
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1112yes—
400C22×C4C23×D1112yes—
401C22×C4C23×D1111yescharacteristic
402Q16—4416no—
403SD16—4416no—
404M16—228no—
405C2×C8—118no—
406C4⋊C4—28no—
407C4⋊C4—28no—
408C4⋊C4—28no—
409C4⋊C4—28no—
410C4⋊C4—114no—
411C4⋊C4—224no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C22⋊C4—222no—
417C22⋊C4—224no—
418C22⋊C4—224no—
419C22⋊C4—224no—
420C22⋊C4—224no—
421C42—222no—
422C42—224no—
423C42C2×C22⋊D1111yescharacteristic
424C42C2×C22⋊D1112yes—
425C42C2×C22⋊D1111yescharacteristic
426C42C2×C22⋊D1112yes—
427C42C2×C22⋊D1112yes—
428C42C2×C22⋊D1112yes—
429C42C2×C22⋊D1112yes—
430C42C23×D1111yescharacteristic
431C42C23×D1111yescharacteristic
432C42C23×D1112yes—
433C11#6080011yescharacteristic, complemented, Sylow
434C23—22no—
435C23—24no—
436C23—222no—
437C23C22×C22⋊D1111yescharacteristic
438C23C22×C22⋊D1112yes—
439Q8—216no—
440Q8—416no—
441Q8—48no—
442Q8—224no—
443Q8—444no—
444D4—224no—
445D4—444no—
446D4—448no—
447D4—444no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—28no—
457C2×C4—416no—
458C2×C4—48no—
459C2×C4—224no—
460C2×C4—222no—
461C2×C4—444no—
462C2×C4—448no—
463C2×C4#6699518yescomplemented
464C2×C4#6703714yes—
465C2×C4C22×C22⋊D1112yes—
466C2×C4C22×C22⋊D1112yes—
467C2×C4C22×C22⋊D1112yes—
468C2×C4C22×C22⋊D1111yescharacteristic
469C2×C4C22×C22⋊D1112yes—
470C2×C4C22×C22⋊D1112yes—
471C2×C4C24×D1111yescharacteristic
472C8—228no—
473C22—28no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—442no—
478C22—444no—
479C22#1062333612yes—
480C22C2×#6699514yes—
481C22C23×C22⋊D1111yescharacteristic
482C4—22no—
483C4—22no—
484C4—22no—
485C4—48no—
486C4—442no—
487C4—444no—
488C4#1062333612yes—
489C4C2×#6699514yes—
490C4C2×#6699514yes—
491C4C2×#6703712yes—
492C2—22no—
493C2—24no—
494C2—882no—
495C2C2×#1062333611yescharacteristic
496C2C22×#6699512yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×C4⋊Q8C2
socleC22×C11C23×D4
prime radical#13081912C2
hypercenterC22×C4⋊Q8D11
hypocenterC11#60800
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13079643C2semidirect
3. #13079564C2semidirect
4. #13079541C2semidirect
5. #13079073C2semidirect
6. #13078996C2semidirect
7. #13078099C2semidirect
8. #13077850C2semidirect
9. #13077249C2semidirect
10. C22×C11×C4⋊Q8C2semidirect
37. #10622705C22semidirect
38. #10622703C22semidirect
39. #10622699C22semidirect
40. #10622698C22semidirect
41. #10622696C22semidirect
42. #10622695C22semidirect
43. #10622694C22semidirect
187. C22×C4⋊Q8D11semidirect
215. C2×C4×C11#137semidirect
433. C11#60800semidirect
463. C2×C4#66995semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130796432
#130795642
#130795412
#130790732
#130789962
#130780992
#130778502
#130772492
C22×C11×C4⋊Q82
#6080011