Finite Group Databasebeta

← M16×#4325 #14725213

Subgroups — M16×#4325 #14725213

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4325C211yesmaximal, characteristic
2M16×D44C211yesmaximal, characteristic
3#13067506C212yesmaximal, complemented
4#13067459C212yesmaximal, complemented
5#13067450C212yesmaximal, complemented
6C8×#4325C212yesmaximal, complemented
7#13067371C211yesmaximal, characteristic, complemented
8#13067045C211yesmaximal, characteristic, complemented
9#13067040C211yesmaximal, characteristic
10M16×C11⋊C8C211yesmaximal, characteristic, complemented
11Q8×C11×M16C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C411yescharacteristic
14C2×M16×D11—21no—
15C2×C4×D44C2211yescharacteristic
16C11×#446—22no—
17C11×#446C2212yescomplemented
18C8×Q8×C11C2212yescomplemented
19C11×#423—21no—
20C11×#423C2211yescharacteristic
21C4×C11×M16—21no—
22C4×C11×M16C2211yescharacteristic
23C2×#66899C411yescharacteristic
24#10622739—21no—
25C4×#4325C411yescharacteristic
26C4×#4325C411yescharacteristic
27C4×#4325C411yescharacteristic
28C4×#4325C411yescharacteristic
29C4×#4325C2211yescharacteristic
30C4×#4325C2211yescharacteristic
31C4×#4325C2211yescharacteristic
32C4×#4325C2211yescharacteristic
33C2×#66873C411yescharacteristic
34C2×#66872C411yescharacteristic
35#10622538C2211yescharacteristic
36#10622537C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622319—22no—
39#10622301C2212yes—
40C8×D44C2212yes—
41Q8⋊(C11⋊C8)C2212yescomplemented
42Q8⋊(C11⋊C8)C2212yescomplemented
43#10622121C2212yes—
44#10622121C2212yes—
45#10622118C2212yescomplemented
46#10622118C2212yescomplemented
47#10622093C2212yescomplemented
48C8×C11⋊C8C2212yescomplemented
49C22×Q8×C11C2×C411yescharacteristic
50C22×D44C2×C411yescharacteristic
51C22×C4×D11—21no—
52C2×C11×M16—21no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D411yescharacteristic
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11C2×C411yescharacteristic
58C4×Q8×C11C2×C411yescharacteristic
59C4×Q8×C11C2311yescharacteristic
60C4×Q8×C11C2311yescharacteristic
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4325—24no—
66C2×#4325C2×C411yescharacteristic
67C2×#4325C2×C411yescharacteristic
68C2×#4325C2×C411yescharacteristic
69C2×#4325C2×C411yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×#4318—21no—
73C22×C11⋊C8C2×C411yescharacteristic
74C22×C11⋊C8C2×C411yescharacteristic
75M16×D11—44no—
76C2×#4313—22no—
77C2×C8×D11—22no—
78C4×D44—21no—
79C4×D44—21no—
80C4×D44C2×C411yescharacteristic
81C4×D44C2×C411yescharacteristic
82C4×D44C2311yescharacteristic
83C4×D44C2311yescharacteristic
84C11×C4⋊C8—22no—
85C11×C4⋊C8—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2312yes—
88C11×#97—22no—
89C11×#97D412yes—
90C4×C8×C11—22no—
91C4×C8×C11C2312yes—
92#66899C2×C411yescharacteristic
93#66899C2×C411yescharacteristic
94#66899C2×C411yescharacteristic
95#66899C2×C411yescharacteristic
96C22⋊(C11⋊C8)—21no—
97(C2×D11)⋊C8—22no—
98(C2×D11)⋊C8—22no—
99#66873C2×C411yescharacteristic
100#66873C2×C411yescharacteristic
101#66873C2×C411yescharacteristic
102#66873C2×C411yescharacteristic
103#66872C2×C411yescharacteristic
104#66872C2×C411yescharacteristic
105#66872C2×C411yescharacteristic
106#66872C2×C411yescharacteristic
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)—21no—
109C4⋊(C11⋊C8)C2312yes—
110C4×C11⋊C8C2×C411yescharacteristic
111C4×C11⋊C8C2×C411yescharacteristic
112C4×C11⋊C8C2312yes—
113C4×C11⋊C8C2311yescharacteristic
114C4×C11⋊C8C2311yescharacteristic
115M16×SD16—111nomaximal, Sylow
116C23×D11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—41no—
120C2×Q8×C11C22×C411yescharacteristic
121C2×Q8×C11C22×C411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×Dic11—21no—
128C2×D44—22no—
129C2×D44—21no—
130C2×D44—41no—
131C2×D44C22×C411yescharacteristic
132C2×D44C22×C411yescharacteristic
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C11×M16—22no—
140C11×M16—42no—
141C11×M16SD1614yescomplemented
142C2×C8×C11—22no—
143C2×C8×C11C2×D412yes—
144C2×C8×C11C2×D412yes—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C22×C411yescharacteristic
151C11×C4⋊C4C22×C411yescharacteristic
152C42×C11—21no—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11C22×C411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11#4111yescharacteristic
159C42×C11C2411yescharacteristic
160#4325—22no—
161#4325—22no—
162#4325—22no—
163#4325M1614yesdirect product factor
164(C2×D11)⋊C4—21no—
165(C2×D11)⋊C4—21no—
166(C2×D11)⋊C4—21no—
167(C2×D11)⋊C4—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11C22×C411yescharacteristic
170C4⋊Dic11C22×C411yescharacteristic
171#4318—42no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—41no—
176C2×C11⋊C8C22×C411yescharacteristic
177C2×C11⋊C8C22×C411yescharacteristic
178C2×C11⋊C8C22×C411yescharacteristic
179C2×C11⋊C8C22×C411yescharacteristic
180#4313—44no—
181C8×D11—44no—
182Q8×M16D1111yescharacteristic, complemented
183C2×C4×SD16—111no—
184D4×M16—111no—
185#1590—112no—
186#1583—112no—
187#1582—112no—
188C8×SD16—112no—
189#1566—111no—
190#1487—111no—
191#1486—111no—
192C8×M16—111no—
193C23×C11C4×D411yescharacteristic
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—81no—
199Q8×C11—21no—
200Q8×C11—21no—
201Q8×C11—21no—
202Q8×C11—42no—
203Q8×C11C2×M1612yescomplemented
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—81no—
213C2×C4×C11C4×D411yescharacteristic
214C2×C4×C11C4×D411yescharacteristic
215C2×C4×C11C4×D411yescharacteristic
216C2×C4×C11C2×SD1612yes—
217C2×C4×C11#13512yes—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—42no—
224D44—21no—
225D44—21no—
226D44—21no—
227D44—42no—
228D44C2×M1612yes—
229C4×D11—41no—
230C4×D11—41no—
231C4×D11—41no—
232C4×D11—41no—
233C4×D11—42no—
234C4×D11—42no—
235C8×C11—22no—
236C8×C11—42no—
237C8×C11C2×SD1614yescomplemented
238C11⋊C8—21no—
239C11⋊C8—21no—
240C11⋊C8—21no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243C11⋊C8C2×M1612yescomplemented
244C22×SD16—111no—
245C22×M16—221no—
246C2×C4×Q8C2×D1111yescharacteristic
247C2×C4×D4—111no—
248#446—22no—
249#446C2×D1112yescomplemented
250C8×Q8C2×D1112yescomplemented
251C4×SD16—111no—
252C4×SD16—111no—
253C4×SD16—111no—
254C4×SD16—111no—
255C4×SD16—111no—
256C4×SD16—111no—
257C4×SD16—111no—
258C4×SD16—111no—
259#436—112no—
260#435—222no—
261C8×D4—112no—
262#431—111no—
263C2×#106—111no—
264#423—21no—
265#423—111no—
266#423C2×D1111yescharacteristic
267C2×#103—111no—
268C2×#102—111no—
269#407—221no—
270C4×M16—21no—
271C4×M16C2×D1111yescharacteristic
272C2×C4×C8—111no—
273#334—112no—
274#334—112no—
275Q8⋊C8—112no—
276Q8⋊C8—112no—
277D4⋊C8—112no—
278D4⋊C8—112no—
279#322—112no—
280C82—112no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11C4×SD1612yes—
284C22×C11C2×C4×D411yescharacteristic
285C2×D11—22no—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—41no—
289C2×D11—41no—
290C2×D11—41no—
291C2×D11—84no—
292C4×C11—21no—
293C4×C11—22no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11C4×SD1612yes—
300C4×C11C22×M1611yescharacteristic
301C4×C11#56811yescharacteristic
302C4×C11C22×SD1611yescharacteristic
303C4×C11C2×#13511yescharacteristic
304Dic11—41no—
305Dic11—41no—
306C22×Q8C4×D1111yescharacteristic
307C22×D4—111no—
308C23×C4—221no—
309C2×SD16—111no—
310C2×SD16—111no—
311C2×SD16—111no—
312C2×SD16—111no—
313C2×SD16—224no—
314C2×M16—21no—
315C2×M16—221no—
316C2×M16—222no—
317C2×M16—444no—
318C2×M16C22⋊D1111yescharacteristic
319C2×M16C22⋊D1111yescharacteristic
320C22×C8—111no—
321C22×C8—111no—
322C22×C8—222no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8C4×D1111yescharacteristic
326C4×Q8C4×D1111yescharacteristic
327C4×Q8C22×D1111yescharacteristic
328C4×Q8C22×D1111yescharacteristic
329C4×D4—111no—
330C4×D4—111no—
331C4×D4—111no—
332C4×D4—111no—
333C4×D4—221no—
334C4×D4—221no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4C4×D1111yescharacteristic
338C2×C22⋊C4—221no—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341#106—111no—
342#106—111no—
343#106—111no—
344#106—111no—
345C4⋊C8—22no—
346C4⋊C8—22no—
347C4⋊C8—21no—
348C4⋊C8—112no—
349C4⋊C8—221no—
350C4⋊C8—221no—
351C4⋊C8C22×D1112yes—
352#103—111no—
353#103—111no—
354#103—111no—
355#103—111no—
356#102—111no—
357#102—111no—
358#102—111no—
359#102—111no—
360C22⋊C8—221no—
361C22⋊C8—222no—
362C22⋊C8—222no—
363#97—22no—
364#97C22⋊D1112yes—
365C4×C8—22no—
366C4×C8—111no—
367C4×C8—111no—
368C4×C8—111no—
369C4×C8—111no—
370C4×C8—112no—
371C4×C8C22×D1112yes—
372C2×C11—22no—
373C2×C11D4×M1611yescharacteristic
374C2×C11C2×C4×SD1611yescharacteristic
375C2×C11#295711yescharacteristic
376D11—42no—
377D11—81no—
378C24—221no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—41no—
382C2×Q8C2×C4×D1111yescharacteristic
383C2×Q8C2×C4×D1111yescharacteristic
384C2×D4—111no—
385C2×D4—111no—
386C2×D4—222no—
387C2×D4—221no—
388C2×D4—441no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4C2×C4×D1111yescharacteristic
399C22×C4#433911yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401SD16—114no—
402SD16—222no—
403SD16—222no—
404SD16—222no—
405M16—22no—
406M16—42no—
407M16—442no—
408M16—444no—
409M16#432514yesdirect product factor
410C2×C8—22no—
411C2×C8—111no—
412C2×C8—111no—
413C2×C8—111no—
414C2×C8—111no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—441no—
419C2×C8—444no—
420C2×C8C2×C22⋊D1112yes—
421C2×C8C2×C22⋊D1112yes—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—111no—
428C4⋊C4—111no—
429C4⋊C4—221no—
430C4⋊C4C2×C4×D1111yescharacteristic
431C4⋊C4C2×C4×D1111yescharacteristic
432C22⋊C4—221no—
433C22⋊C4—221no—
434C22⋊C4—221no—
435C22⋊C4—221no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42—21no—
440C42C2×C4×D1111yescharacteristic
441C42#433911yescharacteristic
442C42C2×C22⋊D1111yescharacteristic
443C42C23×D1111yescharacteristic
444C11M16×SD1611yescharacteristic, complemented, Sylow
445C23—221no—
446C23—221no—
447C23—442no—
448C23—442no—
449C23—881no—
450C23C4×C22⋊D1111yescharacteristic
451Q8—21no—
452Q8—21no—
453Q8—21no—
454Q8—42no—
455Q8M16×D1112yescomplemented
456D4—112no—
457D4—221no—
458D4—221no—
459D4—221no—
460D4—442no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—81no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4C4×C22⋊D1111yescharacteristic
480C2×C4C4×C22⋊D1111yescharacteristic
481C2×C4C4×C22⋊D1111yescharacteristic
482C2×C4C2×#432512yes—
483C2×C4#6700312yes—
484C2×C4C22×C4×D1111yescharacteristic
485C2×C4C2×#433911yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—22no—
488C8—42no—
489C8—112no—
490C8—221no—
491C8—221no—
492C8—221no—
493C8—442no—
494C8—442no—
495C8C2×#432514yescomplemented
496C22—21no—
497C22—21no—
498C22—222no—
499C22—441no—
500C22—441no—
501C22—441no—
502C22—441no—
503C22—441no—
504C22—884no—
505C22C4×#432512yes—
506C22C2×C4×C22⋊D1111yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—22no—
511C4—41no—
512C4—41no—
513C4—41no—
514C4—441no—
515C4—441no—
516C4C4×#432512yes—
517C4C2×M16×D1111yescharacteristic
518C4#1062327611yescharacteristic
519C4C22×#432511yescharacteristic
520C4C2×#6700311yescharacteristic
521C2—22no—
522C2—442no—
523C2—881no—
524C2M16×C22⋊D1111yescharacteristic
525C2C2×C4×#432511yescharacteristic
526C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingQ8×C11×M16C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenterQ8×M16D11
hypocenterC11M16×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
3. #13067506C2semidirect
4. #13067459C2semidirect
5. #13067450C2semidirect
6. C8×#4325C2semidirect
7. #13067371C2semidirect
8. #13067045C2semidirect
10. M16×C11⋊C8C2semidirect
11. Q8×C11×M16C2semidirect
17. C11×#446C22semidirect
18. C8×Q8×C11C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
45. #10622118C22semidirect
46. #10622118C22semidirect
47. #10622093C22semidirect
48. C8×C11⋊C8C22semidirect
141. C11×M16SD16semidirect
163. #4325M16direct (N × H)
182. Q8×M16D11semidirect
203. Q8×C11C2×M16semidirect
237. C8×C11C2×SD16semidirect
243. C11⋊C8C2×M16semidirect
249. #446C2×D11semidirect
250. C8×Q8C2×D11semidirect
409. M16#4325direct (N × H)
444. C11M16×SD16semidirect
455. Q8M16×D11semidirect
495. C8C2×#4325semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
M16×D442
#130675062
#130674592
#130674502
C8×#43252
#130673712
#130670452
#130670402
M16×C11⋊C82
Q8×C11×M162
M16×SD1611