Finite Group Databasebeta

← #14769625

Subgroups — #14769625

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic11C212yesmaximal, complemented
2#13071457C211yesmaximal, characteristic, complemented
3#13071446C211yesmaximal, characteristic, complemented
4#13069472C212yesmaximal, complemented
5#13068966C212yesmaximal, complemented
6#13068959C212yesmaximal, complemented
7#13068641C211yesmaximal, characteristic, complemented
8#13068556C211yesmaximal, characteristic, complemented
9#13068556C211yesmaximal, characteristic, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C22×C11×#135C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C2×C11×#135—28no—
15C2×C11×#135C418yescomplemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×Q8×Dic11C2212yes—
22C2×D4×Dic11C2212yes—
23#10622843C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26#10622834—22no—
27#10622834C2212yes—
28#10622833—22no—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622825—21no—
32#10622825C2211yescharacteristic
33#10622825C2211yescharacteristic
34#10622824—21no—
35C4×C22⋊Dic11—21no—
36C4×C22⋊Dic11C2211yescharacteristic
37C2×C11⋊#95—21no—
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39SD16×Dic11—28no—
40C2×#66881C2212yes—
41C2×C8×Dic11C2212yes—
42#10622189C2212yes—
43#10622188C2212yes—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—42no—
49C2×C11×#41—42no—
50C2×C11×#41C2×C414yes—
51C2×C11×#41C2×C414yescomplemented
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—22no—
62C11×#135—232no—
63C2×C11×Q16—24no—
64C2×C11×Q16C2×C414yescomplemented
65C2×C11×SD16—24no—
66C2×C11×SD16C2×C414yes—
67C2×C11×SD16C2×C414yescomplemented
68C2×C11×SD16D418yes—
69C2×C11×D8—24no—
70C2×C11×D8C2×C414yes—
71C22×C8×C11—24no—
72C22×C8×C11C2×C414yescomplemented
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11D412yes—
81Q8×Dic11—24no—
82Q8×Dic11—42no—
83D4×Dic11—24no—
84D4×Dic11—42no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4×Dic11—22no—
89C2×C4×Dic11C2312yes—
90C22×C11⋊C8C2312yes—
91#66899—24no—
92#66899—42no—
93#66896—24no—
94#66896—42no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95D411yescharacteristic
100C11⋊#95D411yescharacteristic
101C22⋊(C11⋊C8)—22no—
102#66881—24no—
103C8×Dic11—24no—
104#22449—111nomaximal, Sylow
105C24×C11—21no—
106C24×C11—21no—
107C24×C11C2×D411yescharacteristic
108C11×#41—28no—
109C11×#41—28no—
110C11×#41—44no—
111C11×#41—44no—
112C11×#41—48no—
113C11×#41—48no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11C22×C412yes—
120C2×Q8×C11C22×C412yes—
121C2×Q8×C11C2×D414yes—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11C22×C412yes—
132C2×D4×C11C22×C412yes—
133C2×D4×C11C2×D414yes—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—44no—
141C22×C4×C11—44no—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—44no—
149C22×Dic11—44no—
150C22×Dic11—82no—
151C22×Dic11C2×D412yes—
152C22×Dic11C2×D412yes—
153C11×Q16—28no—
154C11×SD16—28no—
155C11×SD16C22⋊C4116yescomplemented
156C11×D8—28no—
157C2×C8×C11—28no—
158C2×C8×C11—22no—
159C2×C8×C11C22×C412yes—
160C2×C8×C11C22×C412yes—
161C2×C8×C11C2×D414yes—
162C22⋊Dic11—24no—
163C22⋊Dic11—44no—
164C22⋊Dic11—44no—
165C22⋊Dic11—81no—
166C22⋊Dic11—81no—
167C22⋊Dic11—82no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—44no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—44no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C22×#135D1111yescharacteristic
180C2×C4×SD16—112no—
181#2341—111no—
182#2339—111no—
183#1968—112no—
184#1879—112no—
185#1878—112no—
186#1807—111no—
187#1788—111no—
188#1788—111no—
189C8×C22⋊C4—111no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—42no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11C4×D412yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—22no—
207Q8×C11—24no—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—42no—
211Q8×C11C2×C22⋊C414yes—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—24no—
216D4×C11—48no—
217D4×C11—48no—
218D4×C11—42no—
219D4×C11C2×C22⋊C414yes—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—48no—
228C2×C4×C11—48no—
229C2×C4×C11—42no—
230C2×C4×C11C4×D412yes—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D412yes—
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)12yes—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—88no—
247C2×Dic11#13514yescomplemented
248C8×C11—22no—
249C8×C11C2×C22⋊C414yes—
250C11⋊C8—42no—
251C22×#41C2×D1111yescharacteristic
252C22×#41C2×D1111yescharacteristic
253C2×#135—28no—
254C2×#135Dic1118yescomplemented
255C22×Q16C2×D1111yescharacteristic
256C22×SD16C2×D1111yescharacteristic
257C22×SD16C2×D1111yescharacteristic
258C22×D8C2×D1111yescharacteristic
259C23×C8C2×D1111yescharacteristic
260C2×C4×Q8—112no—
261C2×C4×D4—112no—
262C4×SD16—228no—
263C2×#106—112no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#102—112no—
267C2×#102—112no—
268C2×C22⋊C8—111no—
269C2×C4×C8—112no—
270#391—112no—
271#390—112no—
272#390—222no—
273#386—222no—
274#381—221no—
275#380—111no—
276#380—111no—
277#380—221no—
278C4×C22⋊C4—111no—
279C4×C22⋊C4—221no—
280C2×#95—221no—
281#340—112no—
282#336—112no—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11C2×C4×D411yescharacteristic
299C22×C11D4212yes—
300C22×C11C2×#13512yes—
301C22×C11#57711yescharacteristic
302C22×C11#57711yescharacteristic
303C4×C11—22no—
304C4×C11—24no—
305C4×C11—42no—
306C4×C11C22×C22⋊C411yescharacteristic
307C4×C11#51811yescharacteristic
308C4×C11#54612yes—
309Dic11—24no—
310Dic11—42no—
311Dic11—82no—
312Dic11—82no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—24no—
316C2×#41—24no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41C2×Dic1114yes—
320C2×#41C2×Dic1114yescomplemented
321C22×Q8C22×D1111yescharacteristic
322C22×Q8C22×D1111yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C22×D1111yescharacteristic
326C22×D4C22×D1111yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—222no—
330C23×C4C22×D1111yescharacteristic
331#135—232no—
332C2×Q16—24no—
333C2×Q16C2×Dic1114yescomplemented
334C2×SD16—24no—
335C2×SD16C2×Dic1114yes—
336C2×SD16C2×Dic1114yescomplemented
337C2×SD16C22⋊D1118yes—
338C2×D8—24no—
339C2×D8C2×Dic1114yes—
340C22×C8—24no—
341C22×C8—112no—
342C22×C8C2×Dic1114yescomplemented
343C22×C8C22×D1111yescharacteristic
344C22×C8C22×D1111yescharacteristic
345C4×Q8—224no—
346C4×Q8—442no—
347C4×D4—224no—
348C4×D4—442no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—222no—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C42—112no—
359C2×C42—222no—
360#106—224no—
361#103—224no—
362#103—442no—
363#102—224no—
364#102—442no—
365C22⋊C8—222no—
366C4×C8—224no—
367#95—111no—
368#95—111no—
369#95—222no—
370#95—222no—
371#95—221no—
372#95—221no—
373C2×C11—42no—
374C2×C11—44no—
375C2×C11—82no—
376C2×C11D4×C22⋊C411yescharacteristic
377C2×C11C4×#13511yescharacteristic
378C2×C11#295211yescharacteristic
379C2×C11#328212yes—
380C2×C11#328412yes—
381C24—21no—
382C24—21no—
383C24D4×D1111yescharacteristic
384#41—28no—
385#41—28no—
386#41—44no—
387#41—44no—
388#41—48no—
389#41—48no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8C22×Dic1112yes—
396C2×Q8C22×Dic1112yes—
397C2×Q8C2×C22⋊D1114yes—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4C22×Dic1112yes—
408C2×D4C22×Dic1112yes—
409C2×D4C2×C22⋊D1114yes—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—444no—
423C22×C4—444no—
424C22×C4—882no—
425C22×C4D4×D1111yescharacteristic
426C22×C4#434112yes—
427C22×C4C22×Dic1112yes—
428C22×C4C23×D1111yescharacteristic
429Q16—28no—
430SD16—28no—
431SD16C22⋊Dic11116yescomplemented
432D8—28no—
433C2×C8—22no—
434C2×C8—28no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8C22×Dic1112yes—
439C2×C8C22×Dic1112yes—
440C2×C8C2×C22⋊D1114yes—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—444no—
446C22⋊C4—224no—
447C22⋊C4—444no—
448C22⋊C4—444no—
449C22⋊C4—882no—
450C22⋊C4—881no—
451C22⋊C4—881no—
452C42—222no—
453C42—222no—
454C42—444no—
455C11#2244911yescharacteristic, complemented, Sylow
456C23—22no—
457C23—21no—
458C23—21no—
459C23—22no—
460C23—24no—
461C23—22no—
462C23—22no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23D4×Dic1112yes—
471C23C2×D4×D1111yescharacteristic
472Q8—22no—
473Q8—24no—
474Q8—22no—
475Q8—22no—
476Q8—42no—
477Q8C2×C22⋊Dic1114yes—
478D4—22no—
479D4—22no—
480D4—24no—
481D4—22no—
482D4—48no—
483D4—48no—
484D4—42no—
485D4C2×C22⋊Dic1114yes—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—48no—
494C2×C4—48no—
495C2×C4—42no—
496C2×C4—114no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—888no—
509C2×C4D4×Dic1112yes—
510C2×C4C2×#434111yescharacteristic
511C2×C4#6703712yes—
512C2×C4C23×Dic1111yescharacteristic
513C2×C4C22×C22⋊D1112yes—
514C8—22no—
515C8—442no—
516C8C2×C22⋊Dic1114yes—
517C22—22no—
518C22—24no—
519C22—22no—
520C22—22no—
521C22—42no—
522C22—44no—
523C22—42no—
524C22—42no—
525C22—44no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22D11×#13512yes—
533C22#1062330111yescharacteristic
534C22#1062330111yescharacteristic
535C22C2×D4×Dic1111yescharacteristic
536C22D4×C22⋊D1112yes—
537C4—22no—
538C4—24no—
539C4—42no—
540C4—224no—
541C4—442no—
542C4—882no—
543C4—882no—
544C4#1062332911yescharacteristic
545C4#1062333712yes—
546C4C22×C22⋊Dic1111yescharacteristic
547C2—42no—
548C2—44no—
549C2—82no—
550C2D4×C22⋊Dic1111yescharacteristic
551C2#135×Dic1111yescharacteristic
552C2#1307750011yescharacteristic
553C2#1308031712yes—
554C2#1308034012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×#135C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC22×#135D11
hypocenterC11#22449
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic11C2semidirect
2. #13071457C2semidirect
3. #13071446C2semidirect
4. #13069472C2semidirect
5. #13068966C2semidirect
6. #13068959C2semidirect
7. #13068641C2semidirect
8. #13068556C2semidirect
9. #13068556C2semidirect
10. C8×C22⋊Dic11C2semidirect
15. C2×C11×#135C4semidirect
51. C2×C11×#41C2×C4semidirect
64. C2×C11×Q16C2×C4semidirect
67. C2×C11×SD16C2×C4semidirect
72. C22×C8×C11C2×C4semidirect
155. C11×SD16C22⋊C4semidirect
247. C2×Dic11#135semidirect
254. C2×#135Dic11semidirect
320. C2×#41C2×Dic11semidirect
333. C2×Q16C2×Dic11semidirect
336. C2×SD16C2×Dic11semidirect
342. C22×C8C2×Dic11semidirect
431. SD16C22⋊Dic11semidirect
455. C11#22449semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic112
#130714572
#130714462
#130694722
#130689662
#130689592
#130686412
#130685562
C8×C22⋊Dic112
C22×C11×#1352
#2244911